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Chapter: 6 -Problem: 16 >> Repeat Problem 15 using MATLAB.Data From Problem 15:Given the unity feedback system of Figure P6.3 withtell how many closed-loop poles are located in the right half-plane, in the left half-plane, and on the j?-axis. Transcribed Image Text: 8 G(s) s(s6 – 255 - s4 + 2s3 + 4s2 - 8s – 4) 00
Answer Preview: To find the locations of the closed loop poles of the given system using MATLAB we can use the pole …

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, Chapter: 3 -Problem: 13 >> If an electrical network has three energy-storage elements, is it possible to have a state-space representation with more than three state variables? Explain.
Answer Preview: yes it is possible to have state space representation with more than three state variab…

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, Chapter: 5 -Problem: 10 >> Name five representations of systems in state space.
Answer Preview: Definition of State Space Models Continuous Tim…

, Chapter: 3 -Problem: 11 >> What factors influence the choice of state variables in any system?
Answer Preview: State variables of a system are the smallest set of …

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, Chapter: 10 -Problem: 12 >> Write a program in MATLAB that will do the following:a. Allow a value of gain, K, to be entered from the keyboardb. Display the Bode plots of a system for the entered value of Kc. Calculate and display the gain and phase margin for the entered value of K Test your program on a unity feedback system with G(s) = K/[s(s + 3)(s + 12)].
Answer Preview: Program to calculate and display the Bode plot gain margin and phase margin of a unity feedback syst…

, Chapter: 12 -Problem: 6 >> Given the following open-loop plant: design a controller to yield 10% overshoot with a peak time of 0.5 second. Use the controller canonical form for state-variable feedback. Transcribed Image Text: 100(s + 2)(s + 25) G(s) = (s + 1)(s + 3)(s +5)
Answer Preview: To design a state variable feedback controller we need to first convert the transfer function of the …

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, Chapter: 9 -Problem: 37 >> The room temperature of an 11 m2 room is to be controlled by varying the power of an indoor radiator. For this specific room, the open-loop transfer function from radiator power, Q? (s), to temperature, T(s), is (Thomas, 2005)The system is assumed to be in the closed-loop configuration shown in Figure P9.1.a. For a unit step input, calculate the steady-state error of the system.b. Try using the pr
Answer Preview: a The steady state error of the system can be calculated using the final value theorem E ss lim s 0 sT s 1 s From the transfer function given in the problem statement we have T s Q s 1 s 4 Therefore E …

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, Chapter: 5 -Problem: 12 >> Which form of the state-space representation leads to a diagonal matrix?
Answer Preview: The diagonal form of the state space representation leads to a diagonal matrix Explana…

, Chapter: 2 -Problem: 65 >> A photovoltaic system is used to capture solar energy to be converted to electrical energy. A control system is used to pivot the solar platform to track the sun’s movements in order to maximize the captured energy. The system consists of a motor and load similar to that discussed in Section 2.8. A model has been proposed (Agee, 2012) that is different from the model developed in the chapter in th
Answer Preview: The transfer function of the augmented system m s Ea s is give…

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, Chapter: 11 -Problem: 27 >> For the heat exchange system described in Problem 39, Chapter 9 (Smith, 2002):a. Design a passive lag-lead compensator to achieve 5% steady-state error with a transient response of 10% overshoot and a settling time of 60 seconds for step inputs.b. Use MATLAB to simulate and verify your design.
Answer Preview: a To design a passive lag lead compensator to achieve 5 steady state error wit…

, Chapter: 4 -Problem: 18 >> Find the damping ratio and natural frequency for each second-order system of Problem 8 and show that the value of the damping ratio conforms to the type of response (underdamped, overdamped, and so on) predicted in that problem.Data From Problem 8:For each of the transfer functions shown below, find the locations of the poles and zeros, plot them on the s-plane, and then write an expression for th
Answer Preview: To find the damping ratio and natural frequency for each second order system we first need to determ…

, Chapter: 2 -Problem: 63 >> A muscle hanging from a beam is shown in Figure P2.37(a) (Lessard, 2009). The ?-motor neuron can be used to electrically stimulate the muscle to contract and pull the mass, m, which under static conditions causes the muscle to stretch. An equivalent mechanical system to this setup is shown in Figure P2.37(b). The force Fiso will be exerted when the muscle contracts. Find an expression for the disp
Answer Preview: ANSWER To solve the problem let s analyze the equivalent mechanical system shown in Figure P2 37 b W…

, Chapter: 6 -Problem: 19 >> Using the Routh-Hurwitz criterion, tell how many closed-loop poles of the system shown in Figure P6.5 lie in the left half-plane, in the right half-plane, and on the j?-axis. Transcribed Image Text: R(s) 450 C(s) 435+10s2+30s+150 FIGURE P6.5
Answer Preview: The system shown in Figure P6 5 can be represented by the transfer function G s 1 s 3 3s 2 2s 1 To u…

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, Chapter: 13 -Problem: 21 >> What characteristic is common between a cascade compensator designed on the s-plane and the digital compensator to which it is converted?
Answer Preview: The lead compensator provides phase lead at high frequencies This shifts the root locus to the left …

, Chapter: 4 -Problem: 31 >> Find the percent overshoot, settling time, rise time, and peak time for Transcribed Image Text: 14.65 T(s) (s2 + 0.842s + 2.93)(s + 5)
Answer Preview: Three basic types of control systems are available to executives 1 output control 2 behavi…

, Chapter: 3 -Problem: 32 >> For Problem 23 in Chapter 1 we developed the functional block diagrams for the cruise control of serial, parallel, and split-powerhybrid electric vehicles (HEV). Those diagrams showed that the engine or electric motor or both may propel the vehicle. When electric motors are the sole providers of the motive force, the forward paths of all HEV topologies are similar. In general, such a forward path
Answer Preview: ANSWER a The basic time domain equations for the block diagram in Figure P3 18 can be wri…

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, Chapter: 6 -Problem: 37 >> Repeat Problem 36 using MATLAB.Data From Problem 36:Given the unity feedback system of Figure P6.3 witha. Find the range of K for stability.b. Find the frequency of oscillation when the system is marginally stable. Transcribed Image Text: Ks(s + 2) (s2 – 4s + 8)(s + 3) G(s) =
Answer Preview: To analyze the stability of the given unity feedback system and find the range of K for stability we …

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, Chapter: 13 -Problem: 21 >> For the digital system shown in Figure P13.5, where G1(s) = K/[s(s + 1)], find the value of K to yield a peak time of 2 seconds if the sampling interval, T, is 0.2 second. Also, find the range of K for stability.                             Transcribed Image Text: C(s) R(s) + G,(s) Sample- and-hold
Answer Preview: Transfer function G1 s K s s 1 Sampling interval T 0 2 seconds Desired peak time Tp 2 seconds To fin…

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, Chapter: 3 -Problem: 8 >> Show that the system of Figure 3.7 in the text yields a fourth-order transfer function if we relate the displacement of either mass to the applied force, and a third-order one if we relate the velocity of either mass to the applied force.Figure 3.7: Transcribed Image Text: D K M2 Frictionless
Answer Preview: To determine the transfer function of the system in Figure 3 7 we need to write the equations of mot…

, Chapter: 7 -Problem: 9 >> A system has Kp = 4. What steady-state error can be expected for inputs of 70u(t) and 70tu(t)?
Answer Preview: The steady state error of a system with Kp 4 can be calculated by us…

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, Chapter: 4 -Problem: 46 >> Using classical (not Laplace) methods only, solve for the state-transition matrix, the state vector, and the output of the system represented here. Transcribed Image Text: x; y= [1 2]x; -1 -5 x(0) =
Answer Preview: To solve for the state transition matrix the state vector and the output of the system represented b…

, Chapter: 3 -Problem: 1 >> Represent the electrical network shown in Figure P3.1 in state space, where vo(t) is the output. Transcribed Image Text: 12 32 12 v,(1) 2 H 1H 0.5 F FIGURE P3.1
Answer Preview: Represent the electrical network shown in Figure P3 1 in state space where v t is the output 1 v 1 1 …

, Chapter: 1 -Problem: 5 >> A dynamometer is a device used to measure torque and speed and to vary the load on rotating devices. The dynamometer operates as follows to control the amount of torque: A hydraulic actuator attached to the axle presses a tire against a rotating flywheel. The greater the displacement of the actuator, the greater the force that is applied to the rotating flywheel. A strain gage load cell senses the
Answer Preview: Unfortunately I am unable to create a functional block diagram as it requires visual representation …

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, Chapter: 9 -Problem: 30 >> For the unity feedback system in Figure P9.1, withdo the following:a. Design rate feedback to yield a step response with no more than 15% overshoot and no more than 3 seconds settling time. Use Approach 1.b. Use MATLAB and simulate your compensated system. Transcribed Image Text: K G(s) = s(s + 2)(s
Answer Preview: The system in Figure P9 1 is a unity feedback system with an open loop transfer function of G s K s 3 In order to design rate feedback for the system …

, Chapter: 13 -Problem: 3 >> Name two important considerations in analog-to-digital conversion that yield errors.
Answer Preview: There are mainly two types of methods that are commonly …

, Chapter: 4 -Problem: 19 >> A system has a damping ratio of 0.15, a natural frequency of 20 rad/s, and a dc gain of 1. Use inverse Laplace transforms to find an analytic expression of the response of the system to a unit-step input.
Answer Preview: The response of a system with all initial conditions e…

, Chapter: 3 -Problem: 23 >> A linear, time-invariant model of the hypothalamic pituitary-adrenal axis of the endocrine system with five state variables has been proposed as follows (Kyrylov, 2005):where each of the state variables represents circulatory concentrations as follows:x0 = corticotropin-releasing hormonex1 = corticotropinx2 = free cortisolx3 = albumin-bound cortisolx4 = corticosteroid-binding globulind0 = an exter
Answer Preview: The state variables in the given system are x0 x1 x2 x3 and x4 In matrix form the system can be ex…

, Chapter: 1 -Problem: 1 >> A variable resistor, called a potentiometer, is shown in Figure. The resistance is varied by moving a wiper arm along a fixed resistance. The resistance from A to C is fixed, but the resistance from B to C varies with the position of the wiper arm. If it takes 10 turns to move the wiper arm from A to C, draw a block diagram of the potentiometer showing the input variable, the output variable, and
Answer Preview: Q t Vo t r 1 V t V t B Voltage gradient 50 50 L 100 L As the arm m…

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, Chapter: 12 -Problem: 3 >> Different signal-flow graphs can represent the same system. Which form facilitates the calculation of the variable gains during controller design?
Answer Preview: SFG is a diagram which represents a set of equations It consists of nodes and branches such that e…

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, Chapter: 2 -Problem: 4 >> Repeat Problem 20 in Chapter 1, using Laplace transforms. Assume that the forcing functions are zero prior to t = 0-.Data From Problem 20 in Chapter 1:Solve the following differential equations using classical methods. Assume zero initial conditions.a. dx/dt + 7x = 5 cos 2tb. d2x/dt2 + 6dx/dt + 8x = 5 sin 3tc. d2x/dt2 + 8dx/dt + 25x = 10u(t)
Answer Preview: a dx dt Apply lap lace transform 5S x s s 7 S 4 5S x s A 7x 5 cos 2t S 7 S 4 35 53 x s x s 35 53 S 7 …

, Chapter: 6 -Problem: 54 >> A Butterworth polynomial is of the formUse the Routh-Hurwitz criteria to find the zeros of a Butterworth polynomial for:a. n = 1;b. n = 2 Transcribed Image Text: B.0) = 1 +(-1r()". 2n ,n>0
Answer Preview: The Routh Hurwitz criterion can be used to determine the number of roots of a polynomial that lie in …

, Chapter: 10 -Problem: 7 >> A system with only four poles and no zeros would exhibit what value of slope at high frequencies in a Bode magnitude plot?
Answer Preview: An n th order pole has a slope of 20n dB decade The phase plot is at 0 until …

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, Chapter: 4 -Problem: 3 >> In a system with an input and an output, what poles generate the steady-state response?
Answer Preview: The input poles generates the steady s…

, Chapter: 2 -Problem: 3 >> Repeat Problem 19 in Chapter 1, using Laplace transforms. Assume zero initial conditions.Data From Problem 19 in Chapter 1:Repeat Problem 18 using the network shown in Figure P1.7. Assume R=1?; L=0.5H; and1/LC = 16.Data From Problem 18:Given the electric network shown in Figure.a. Write the differential equation for the network if v(t) = u(t), a unit step.b. Solve the differential equation for the
Answer Preview: a Write the differential equation for the network if v t u t a unit step The differential e…

, Chapter: 5 -Problem: 59 >> Use LabVIEW’s Control Design and Simulation Module to obtain the controller and the observer canonical forms for: Transcribed Image Text: s? + 7s+2 s3 + 9s? + 26s + 24 G(s) =
Answer Preview: Controller Canonical Form The controller canonical form is a specific state space representation of …

, Chapter: 6 -Problem: 36 >> Given the unity feedback system of Figure P6.3 witha. Find the range of K for stability.b. Find the frequency of oscillation when the system is marginally stable. Transcribed Image Text: Ks(s + 2) (s2 – 4s + 8)(s + 3) G(s) =
Answer Preview: ANSWER a To determine the range of K for stability we need to analyze the poles of the system The cl…

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, Chapter: 2 -Problem: 61 >> In order to design an underwater vehicle that has the characteristics of both a long-range transit vehicle (torpedo-like) and a highly maneuverable low-speed vehicle (boxlike), researchers have developed a thruster that mimics that of squid jet locomotion (Krieg, 2008). It has been demonstrated there that the average normalized thrust due to a command step input, U(s) = Tref/s is given by:T(t) = T
Answer Preview: T s Tref 1 e t a sin 2f t T s T…

, Chapter: 2 -Problem: 5 >> Repeat Problem 21 in Chapter 1, using Laplace transforms. Use the following initial conditions for each part as follows:(a) x (0) = 4; x´(0) = -4;(b) x(0) = 4; x´(0) = 1;(c) x(0) = 2; x´(0) = 3, where x´(0) = dx/dt(0).Assume that the forcing functions are zero prior to t(0).Data From Problem 21 in Chapter 1:Solve the following differential equations using classical methods and the given initial co
Answer Preview: Laplace transforms can be used to solve linear differential equations with constant coefficients To …

, Chapter: 6 -Problem: 14 >> If a seventh-order system has a row of zeros at the s3 row and two sign changes below the s4 row, how many j? poles does the system have?
Answer Preview: If a seventh order system has a row of zeros at the s 3 row and two sign changes below the …

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, Chapter: 3 -Problem: 7 >> What is required to represent a system in state space?
Answer Preview: In control engineering a state space representation is a mathematical model of a phys…

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, Chapter: 10 -Problem: 2 >> Define frequency response as applied to a physical system.
Answer Preview: Define frequency response as applied to a physical system A …

, Chapter: 12 -Problem: 4 >> In order to effect a complete controller design, a system must be controllable. Describe the physical meaning of controllability.
Answer Preview: The system is said to be controllable if an input can be found that takes any st…

, Chapter: 3 -Problem: 14 >> What is meant by the phase-variable form of the state equation?
Answer Preview: Phase variables The phase variables are defined as th…

, Chapter: 1 -Problem: 12 >> Tactile feedback is an important component in the learning of motor skills such as dancing, sports, and physical rehabilitation. A suit with white dots recognized by a vision system to determine arm joint positions with millimetric precision was developed. This suit is worn by both teacher and student to provide position information. (Lieberman, 2007). If there is a difference between the teacher’
Answer Preview: The system consists of the following components Vision system This component captures the movements …

, Chapter: 7 -Problem: 12 >> For a step input disturbance at the input to the plant, describe the effect of controller and plant gain upon minimizing the effect of the disturbance.
Answer Preview: The effect of the controller and plant gain upon minimizing the effect of th…

, Chapter: 9 -Problem: 34 >> Identify and realize the following controllers with operational amplifiers.a. s + 0.01/sb. s + 2
Answer Preview: a The controller realized with an operational amplifier is given by s 0 01 s 1 0 01…

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, Chapter: 2 -Problem: 28 >> Find the transfer function, G(s) = X3(s)/F(s), for the translational mechanical system shown in Figure P2.13. Transcribed Image Text: 2 N-s/m x3(1) 2 N-s/m x(1) 6 N/m 4 kg 4 kg 6 N/m 2 N-s/m 0000 4 kg Frictionless FIGURE P2.13
Answer Preview: 4 sX s 2 s X s 6 X s 4 sX s 2 s X s 2 s X s 6 X s F s m Equation m X …

, Chapter: 6 -Problem: 27 >> For the unity feedback system of Figure P6.3 withfind the range of K for stability. Transcribed Image Text: K(s + 1) G(s) = %3D
Answer Preview: open loop transfer function G s K s 1 s 4 s 4 unity feedback H s 1 characteristics equat…

, Chapter: 12 -Problem: 7 >> Given the following open-loop plant:design a controller to yield a10%overshoot and a settling time of 2 seconds. Place the third pole 10 times as far from the imaginary axis as the dominant pole pair. Use the phase variables for state-variable feedback. Transcribed Image Text: 20(s + 2) s(s+ 5)(s +
Answer Preview: To design a controller for the open loop plant we will follow these steps Step 1 Analyze the Open Lo…

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, Chapter: 4 -Problem: 2 >> Find the output response, c(t), for each of the systems shown in Figure P4.1. Also find the time constant, rise time, and settling time for each case. Transcribed Image Text: 5 C(s) s+5 (a) 20 C(s) s+ 20 (b) FIGURE P4.1
Answer Preview: a For the transfer function G s 1 s the output response C s is given by C s G s R s 1 s R s For the …

, Chapter: 10 -Problem: 6 >> Each pole of a system contributes how much of a slope to the Bode magnitude plot?
Answer Preview: The corner frequency associated with pol…

, Chapter: 12 -Problem: 38 >> a. Design an observer for the neutralization system using the continuous stirred tank reactor of Problem 35. The observer should have time constants 10 times smaller than those of the original system. Assume that the original state variables are those obtained in the phase-variable representation.b. Simulate your system and observer for a unit step input using Simulink. Assume that the initial con
Answer Preview: To design an observer for the neutralization system using the continuous stirred tank reactor we need to follow the given specifications Let s assume …

, Chapter: 2 -Problem: 32 >> For each of the rotational mechanical systems shown in Figure P2.17, write, but do not solve, the equations of motion. Transcribed Image Text: 0,(1) 8 N-m-s/rad FO s kg-m? 1 N-m-s/rad T(t) 0,(1) 3 kg-m2 3 N-m/rad 9 N-m/rad (a) T(t) D2 DI J3 000 K3 KI ? (b) FIGURE P2.17
Answer Preview: Writing the equations of motion 5s 2 9s 9 1 s s 9 2 s 0 s 9 1 s 3s 2 s 12 2 …

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, Chapter: 9 -Problem: 16 >> A unity feedback control system has the following forward transfer function:a. Design a lead compensator to yield a closed-loop step response with 20.5% overshoot and a settling time of 3 seconds. Be sure to specify the value of K.b. Is your second-order approximation valid?c. Use MATLAB or any other computer program to simulate and compare the transient response of the compensated system to the p
Answer Preview: a To design a lead compensator for the given system to achieve a closed loop step response with 20 5 overshoot and a settling time of 3 seconds follow …

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, Chapter: 12 -Problem: 23 >> Consider the plant whose phase variables are not available. Design an observer for the phase variables with a transient response described by ? = 0.6 and ?n = 120. Do not convert to observer canonical form. Transcribed Image Text: (s + 2) G(s : (s + 5)(s+9)
Answer Preview: State observation technique can be used to design an observer for a plant whose phase variables are not available For the design of the observer we fi…

, Chapter: 3 -Problem: 25 >> Experiments to identify precision grip dynamics between the index finger and thumb have been performed using a ball-drop experiment. A subject holds a device with a small receptacle into which an object is dropped, and the response is measured (Fagergren, 2000). Assuming a step input, it has been found that the response of the motor subsystem together with the sensory system is of the formConvert
Answer Preview: To convert the transfer function to a state space representation we can use the following steps Writ…

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, Chapter: 2 -Problem: 38 >> Find the transfer function, G(s) = ?4(s)/T(s), for the rotational system shown in Figure P2.23. Transcribed Image Text: O0) 26 N-m-s/rad N1 = 26 N4 = 120 N2 = 110 N3 = 23 2 N-m/rad FIGURE P2.23
Answer Preview: Reflecting the forces on 2 NM rad spring T t 0 t 03 t Equation of mot…

, Chapter: 12 -Problem: 28 >> Use MATLAB to design the observer gains for the system given in Problem 27. Data from Problem 27Design an observer for the plant represented in cascade form. Transform the plant to observer canonical form for the design. Then transform the design back to cascade form. The characteristic polynomial for the observer is to be s3 + 600s2 + 40,000s + 1,500,000.
Answer Preview: To design the observer gains for the system given in Problem 27 we will use MATLAB Step 1 Define the …

, Chapter: 3 -Problem: 7 >> Represent the system shown in Figure P3.7 in state space where the output is ?L(t). Transcribed Image Text: T() N1 = 30 2 N-m/rad 3 N-m-s/rad TO N-m/rad N2 = 3000000 N3 = 10 fam N4 = 100 200 N-m-s/rad FIGURE P3.7
Answer Preview: Represent the system in state space where the output …

, Chapter: 6 -Problem: 40 >> Given the unity feedback system of Figure P6.3 witha. Find the range of K for stability.b. Find the frequency of oscillation when the system is marginally stable. Transcribed Image Text: K G(s) = (s+ 49)(s2 + 4s +5)
Answer Preview: a To find the range of K for stability we can use the Routh Hurwitz criterion The characteristic equ…

, Chapter: 10 -Problem: 12 >> Briefly state the Nyquist criterion.
Answer Preview: Nyquist stability criterion states the number of …

, Chapter: 8 -Problem: 39 >> Sketch the root locus for the system of Figure P8.12 and find the following:a. The range of gain to yield stabilityb. The value of gain that will yield a damping ratio of 0.707 for the system’s dominant polesc. The value of gain that will yield closed-loop poles that are critically damped Transcribed Image Text:
Answer Preview: a To sketch the root locus we first find the open loop transfer function of the system G s K s 4 s 1 …

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, Chapter: 2 -Problem: 62 >> The Gompertz growth model is commonly used to model tumor cell growth. Let v(t) be the tumor’s volume, thenwhere ? and ? are two appropriate constants (Edelstein- Keshet, 2005).a. Verify that the solution to this equation is given by v(t) = v0e?/?(1 -e-?t), where v0 is the initial tumor volume.b. This model takes into account the fact that when nutrients and oxygen are scarce at the tumor’s core,
Answer Preview: a To verify the solution v t v0e 1 e t we can differentiate it with respect to t and check if it sat…

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, Chapter: 9 -Problem: 47 >> Steam-driven power generators rotate at a constant speed via a governor that maintains constant steam pressure in the turbine. In addition, automatic generation control (AGC) or load frequency control (LFC) is added to ensure reliability and consistency despite load variations or other disturbances that can affect the distribution line frequency output. A specific turbine-governor system can be de
Answer Preview: a To find the value of K that results in a dominant pole with 0 7 we need to determine the desired damping ratio and natural frequency of the closed loop system The closed loop transfer function of th…

, Chapter: 8 -Problem: 21 >> For the unity feedback system of Figure P8.3, wheresketch the root locus and find the following:a. The breakaway and break-in pointsb. The j?-axis crossingc. The range of gain to keep the system stabled. The value of K to yield a stable system with second order complex poles, with a damping ratio of 0.5. Transcribed Image
Answer Preview: a 1 d 1 1 d 2 1 d 1 d 1 Breakaway 0 37 for K 0 07 Break in 1 37 …

, Chapter: 12 -Problem: 13 >> In Section 12.4, we discussed how to design a controller for systems not represented in phase-variable form with its typical lower companion matrix. We described how to convert the system to phase-variable form, design the controller, and convert back to the original representation. This technique can be applied just as easily if the original representation is converted to controller canonical for
Answer Preview: In Example 12 4 of the text we designed a controller for the following uncompensated plant G s s 1 s …

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, Chapter: 6 -Problem: 31 >> Use the Routh-Hurwitz criterion to find the range of K for which the system of Figure P6.6 is stable. Transcribed Image Text: R(s) + E(s) C(s) K(s? – 2s + 2) 1 s2 + 2s +4 FIGURE P6.6
Answer Preview: The closed loop transfer function for the given system is Fr…

, Chapter: 10 -Problem: 11 >> For a system with three poles at 4, what is the maximum difference between the asymptotic approximation and the actual magnitude response?
Answer Preview: The maximum difference between the asymptotic approximation and the actual magnitude re…

, Chapter: 8 -Problem: 64 >> Harmonic drives are very popular for use in robotic manipulators due to their low backlash, high torque transmission, and compact size (Spong, 2006). The problem of joint flexibility is sometimes a limiting factor in achieving good performance. Consider that the idealized model representing joint flexibility is shown in Figure P8.18. The input to the drive is from an actuator and is applied at ?m.
Answer Preview: To find the gain KD that yields an approximate 5 overshoot in the step response we can u…

, Chapter: 12 -Problem: 6 >> In order to determine controllability mathematically, the controllability matrix is formed, and its rank evaluated. What is the final step in determining controllability if the controllability matrix is a square matrix?
Answer Preview: The system is controllable if the rank of Q c is …

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, Chapter: 9 -Problem: 45 >> Given the system shown in Figure P9.10, find the values of K and Kf so that the closed-loop dominant poles will have a damping ratio of 0.5 and the underdamped poles of the minor loop will have a damping ratio of 0.8. Transcribed Image Text: Power amplifier and Amplifier plant R(s) E(s) C(s) K Tacho
Answer Preview: The high frequency asymptote for the Bode magnitude plot for a first order highpass filter is …

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, Chapter: 12 -Problem: 13 >> From what equation do we find the characteristic equation of the controller compensated system?
Answer Preview: Solution In order to get characteristic equation 1 KL s 0 we need to …

, Chapter: 3 -Problem: 22 >> In the past, Type-1 diabetes patients had to inject themselves with insulin three to four times a day. New delayed-action insulin analogues such as insulin Glargine require a single daily dose. A similar procedure to the one described in the Pharmaceutical Drug Absorption case study of this chapter is used to find a model for the concentration-time evolution of plasma for insulin Glargine. For a s
Answer Preview: ANSWER a To find the transfer function we can use the standard formula G s C sI A 1 B D where s is t…

, Chapter: 7 -Problem: 10 >> The forward transfer function of a control system has three poles at -1; -2; and -3. What is the system type?
Answer Preview: The system type is an oscillatory system E…

, Chapter: 10 -Problem: 18 >> What simplification to the Nyquist criterion can we usually make for systems that are open-loop unstable?
Answer Preview: The Nyquist criterion simplifies to the Bode stability criterion for systems that are open loop u…

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, Chapter: 2 -Problem: 13 >> Use MATLAB to generate the transfer function:in the following ways:a. The ratio of factors;b. The ratio of polynomials. Transcribed Image Text: 5(s+ 15)(s+ 26)(s+ 72) G(s) = s(s+ 55)(s + 5s+ 30)(s+ 56)(s? + 27s+ 52)
Answer Preview: Here s how you can generate the transfer function in MATLAB for both a ratio o…

, Chapter: 6 -Problem: 45 >> For the transfer function below, find the constraints on K1 and K2 such that the function will have only two j? poles. Transcribed Image Text: K1s + K2 T(s) = s4 + K1s + s? + K2s + 1
Answer Preview: The transfer function T s has a fourth order polynomial in the denominator so it has four poles To h…

, Chapter: 9 -Problem: 8 >> Design a PD controller for the system shown in Figure P9.2 to reduce the settling time by a factor of 4 while continuing to operate the system with 20.5% overshoot. Compare the performance of the compensated system to that of the uncompensated system. Summarize the results in a table similar to that in Example 9.7. Transcr
Answer Preview: The parameters for the uncomp ens ated system can be found u…

, Chapter: 12 -Problem: 15 >> In order to effect a complete observer design, a system must be observable. Describe the physical meaning of observability.
Answer Preview: Observability is the ability to measure the intern…

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, Chapter: 7 -Problem: 15 >> Define, in words, sensitivity and describe the goal of feedback-control-system engineering as it applies to sensitivity.
Answer Preview: Sensitivity is a measure of how a system responds to an input It is the ratio …

, Chapter: 12 -Problem: 7 >> What is an observer?
Answer Preview: Observers are used to estimate the values of the stochastic process given a particular …

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, Chapter: 6 -Problem: 29 >> Find the range of gain, K, to ensure stability in the unity feedback system of Figure P6.3 with Transcribed Image Text: K(s+ 2) (s2 + 1)(s +4)(s - 1) G(s) = R(s) + E(s) C(s) G(s) FIGURE P6.3
Answer Preview: The characteristic equation for a given open loop t…

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, Chapter: 7 -Problem: 4 >> For the system shown in Figure P7.3, what steady-state error can be expected for the following test inputs:10u(t); 10tu(t); 10t2u(t). Transcribed Image Text: R(s) + 3 C(s) s+4 2 6s FIGURE P7.3
Answer Preview: Step 1 …

, Chapter: 13 -Problem: 2 >> Repeat all parts of Problem 1 using MATLAB and MATLAB’s Symbolic Math Toolbox. Data from Problem 1Derive the z-transforms for the time functions listed below. Do not use any z-transform tables. Use the plan f (t) ? f *(t) ? F*(s) ? F(z), followed by converting F(z) into closed form making use of the fact that 1/(1 - z-1) = 1 + z-1 + z-2 + z-3 + ? ? ? . Assume ideal sampling.a. e-atu(t)b. u(t)c. t2
Answer Preview: a F z e a z b F z 1 1 z 1 c F z z 2 e a z d F z z e iw z 1 z 2 MATLAB Solution a sym…

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, Chapter: 6 -Problem: 69 >> Figure P6.18 shows the HEV system, where parameter values have been substituted.It is assumed here that the speed controller has a proportional gain, Kp, to be adjusted. Use the Routh-Hurwitz stability method to find the range of positive Kp for which the system is closed-loop stable (Graebe, 1995). Transcribed Image Text:
Answer Preview: To apply the Routh Hurwitz stability criterion we need to obtain the characteristic equation of the …

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, Chapter: 3 -Problem: 6 >> Represent the rotational mechanical system shown in Figure P3.6 in state space, where ?1(t) is the output. Transcribed Image Text: T(t) 0,(1) 50 kg-m2 N1 = 30 N2 = 10000000 100 kg-m? HE 100 N-m/rad 100 N-m-s/rad FIGURE P3.6
Answer Preview: Drawing the equivalent network image below Writing the equations of motion 555 56s 2 100 theta 2 100 …

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, Chapter: 11 -Problem: 21 >> Given a unity feedback system withdesign a PID controller to yield zero steady-state error for a ramp input, as well as a 20% overshoot, and a peak time less than 1.8 seconds for a step input. Use only frequency response methods.  Transcribed Image Text: K G(s) : s(s + 1.75)(s +6)
Answer Preview: ANSWER To design a PID controller using frequency response methods we will follow these steps Find the open loop transfer function of the system Deter…

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, Chapter: 7 -Problem: 2 >> A position control, tracking with a constant difference in velocity, would yield how much position error in the steady state?
Answer Preview: A position control tracking with a constant difference in veloc…

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, Chapter: 2 -Problem: 11 >> The motor’s transfer function relates armature displacement to armature voltage. How can the transfer function that relates load displacement and armature voltage be determined?
Answer Preview: The speed of DC motor is directly proportional to armature voltage and inversely propor…

, Chapter: 7 -Problem: 11 >> What effect does feedback have upon disturbances?
Answer Preview: Feed back helps to reduce the effect of disturbances on the system Feedback is a pr…

, Chapter: 13 -Problem: 28 >> a. Convert the heading control for the UFSS vehicle shown on the back endpapers (Johnson, 1980) into a digitally controlled system.b. Find the closed-loop pulse transfer function, T(z), if T = 0.1 second.c. Find the range of heading gain to keep the digital system stable.
Answer Preview: a To convert the heading control for the UFSS vehicle into a digitally controlled system the first s…

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, Chapter: 12 -Problem: 1 >> Briefly describe an advantage that state-space techniques have over root locus techniques in the placement of closed-loop poles for transient response design.
Answer Preview: There are three obvious benefits of state space design 1 Unlike the root locus system all pole posit…

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, Chapter: 2 -Problem: 7 >> If we understand the form the mechanical equations take, what step do we avoid in evaluating the transfer function?
Answer Preview: Frequency domain transfer functions describe the rela…

, Chapter: 12 -Problem: 9 >> Repeat Problem 7 assuming that the plant is represented in the parallel form. Do not convert to phase-variable form. Data from Problem 7Given the following open-loop plant:design a controller to yield a10%overshoot and a settling time of 2 seconds. Place the third pole 10 times as far from the imaginary axis as the dominant pole pair. Use the phase variables for state-variable feedback.
Answer Preview: To solve this problem we will use state space representation with the parallel form of the plant The parallel form of the plant is given by A 5 0 0 1 …

, Chapter: 2 -Problem: 31 >> For the unexcited (no external force applied) system of Figure P2.16, do the following:a. Write the differential equation that describes the system.b. Assuming initial conditions x(0) = x0 and x?(0) = x1, write a Laplace transform expression for X(s).c. Find x(t) by obtaining the inverse Laplace transform from the result in Part c.
Answer Preview: A The Differential Equation That Describes the System Md 2 x t dt 2 k x t 0 A…

, Chapter: 10 -Problem: 15 >> For each closed-loop system with the following performance characteristics, find the closed-loop bandwidth:a. ? = 0:2; Ts = 3 secondsb. ? = 0:2; Tp = 3 secondsc. Ts = 4 seconds; Tp = 2 secondsd. ? = 0:3; Tr = 4 seconds:
Answer Preview: The closed loop bandwidth of a system is defined as the frequency at which the magnitude of the clos…

, Chapter: 8 -Problem: 38 >> For the system shown in Figure P8.11, do the following:a. Sketch the root locus.b. Find the j?-axis crossing and the gain, K, at the crossing.c. Find the real-axis breakaway to two-decimal-place accuracy.d. Find angles of arrival to the complex zeros.e. Find the closed-loop zeros.f. Find the gain, K, for a closed-loop step response with 30% overshoot.g. Discuss the validity of your second-order ap
Answer Preview: To sketch the root locus we need to analyze the given transfer function C s K R s s 2 s 3 Where R s 45 8 s 2 2s 5 To start let s find the poles and zeros of the transfer function Poles denominator roo…

, Chapter: 13 -Problem: 20 >> Describe how digital compensators can be designed on the s-plane.
Answer Preview: A compensator is a component in the control system …

, Chapter: 2 -Problem: 22 >> Find the transfer function, G(s) = Vo(s)/Vi(s), for each operational amplifier circuit shown in Figure P2.7. Transcribed Image Text: 100 kQ 2 µF ? 500 k2 2 µF 100 k2 100 k2 2 µF ? (1)'a 100 k2 2 uF (b)
Answer Preview: A R Vi t WW 500 Node equation at Node A O Vi s 1 SC 1 …

, Chapter: 9 -Problem: 11 >> When compensating for steady-state error, what effect is sometimes noted in the transient response?
Answer Preview: A high pass filter HPF is an electronic filter that passes signals with a frequency higher t…

, Chapter: 2 -Problem: 39 >> For the rotational system shown in Figure P2.24, find the transfer function, G(s) = ?L(s)/T(s).Figure P2.24 Transcribed Image Text: 2 N-m-s/rad 2 N-m/rad N2 = 20 A 1 kg-m2 E0000 N3 = 40 N1 = 5 N4= 10 0.02 N-m-s/rad
Answer Preview: Reflect T s and impedance to respective side T s 4 T s And …

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, Chapter: 3 -Problem: 31 >> Problem 67 in Chapter 2 introduced a model for HIV infection. If retroviral drugs, RTIs and PIs as discussed in Problem22 in Chapter 1, are used, the model is modified as follows (Craig, 2004):where 0 ? u1 ? 1, 0 ? u2 ? 1 represent the effectiveness of the RTI and PI medication, respectively.a. Obtain a state-space representation of the HIV/AIDS model by linearizing the equations about theequilibr
Answer Preview: Thorough calculations and explanations SurveyMonkey allows users to buy targeted responses for …

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, Chapter: 13 -Problem: 6 >> What does the inverse z-transform of a time waveform actually yield?
Answer Preview: The signal can be converted from time domain into z do…

, Chapter: 4 -Problem: 1 >> Derive the output responses for all parts of Figure 4.7. Transcribed Image Text: System Pole-zero plot Response G(s) R(s) = C(s) s2+ as + b General c(1) c(t) = 1 +0.17le 7854 1.0 ja 1.17leL146t G(s) S-plane R(s) =3 (b) C(s) 9 0.5 2+ 9s +9 -7.854 -1.146 Overdamped 2 3 4 5 c(1) c(1) = 1-e(cosv8r + sin
Answer Preview: Figure 4 7 represents a logic circuit with three inputs A B and C and two outputs F and G The circui…

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, Chapter: 4 -Problem: 2 >> What does the performance specification for a first-order system tell us?
Answer Preview: It is a system whose dynamic behavior is described by a fir…

, Chapter: 10 -Problem: 1 >> Name four advantages of frequency response techniques over the root locus.
Answer Preview: i Calculation is eary in frequency domain ii Frequunty domain gives you a better …

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, Chapter: 12 -Problem: 9 >> Briefly describe the configuration of an observer.
Answer Preview: In control theory a state observer or state estimator is …

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, Chapter: 8 -Problem: 32 >> For the unity feedback system shown in Figure 8.3, wheredo the following:a. Sketch the root locus.b. Find the value of K that will yield a 10% overshoot.c. Locate all nondominant poles. What can you say about the second order approximation that led to your answer in Part b?d. Find the range of K that yields a stable system.
Answer Preview: ANSWER To solve the given problem we ll follow the steps outlined for each part a Sketch the root locus The root locus plot shows the movement of the …

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, Chapter: 3 -Problem: 18 >> Given the dc servomotor and load shown in Figure P3.11, represent the system in state space, where the state variables are the armature current, ia, load displacement, ?L, and load angular velocity,?L. Assume that the output is the angular displacement of the armature. Do not neglect armature inductance. Transcribed Image
Answer Preview: Since T m J eq frac d omega m dt D eq omega m Tm Jeqdtdm Deqm and T m K t i a Tm Ktia J eq frac d om…

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, Chapter: 4 -Problem: 3 >> Plot the step responses for Problem 2 using MATLAB.Data From Problem 2:Find the output response, c(t), for each of the systems shown in Figure P4.1. Also find the time constant, rise time, and settling time for each case. Transcribed Image Text: 5 C(s) s+5 (a) 20 C(s) s+ 20 (b) FIGURE P4.1
Answer Preview: analyze the response of the control systems in both the time domain and the frequency domain We will …

, Chapter: 9 -Problem: 9 >> In order to speed up a system without changing the percent overshoot, where must the compensated system’s poles on the s-plane be located in comparison to the uncompensated system’s poles?
Answer Preview: If the typical phase margin is around 60 degrees then the minimum phase margin will typica…

, Chapter: 8 -Problem: 65 >> Using LabVIEW, the Control Design and Simulation Module, and the Math Script RT Module, open and customize the Interactive Root Locus VI from the Examples to implement the system of Problem 64. Select the parameter KD to meet the requirement of Problem 64 by varying the location of the closed-loop poles on the root locus. Be sure your front panel shows the following: (1) open-loop transfer functio
Answer Preview: 1 Open Interactive Root Locus VI Open LabVIEW Go to the Example Finder to locate the Interactive Root Locus VI example under the Control and Simulatio…

, Chapter: 12 -Problem: 8 >> Repeat Problem 4 assuming that the plant is represented in the cascade form. Do not convert to phase-variable form. Data from Problem 4Given the following open-loop plant,  design a controller to yield a 10% overshoot and a settling time of 0.5 second. Place the third pole 10 times as far from the imaginary axis as the dominant pole pair. Use the phase variables for state-variable feedback.
Answer Preview: To represent the given open loop plant in cascade form we can first factorize the denominator of G s …

, Chapter: 2 -Problem: 12 >> A system is described by the following differential equation:with the initial conditions x(0) = 1; x: (0) = -1. Show a block diagram of the system, giving its transfer function and all pertinent inputs and outputs. Transcribed Image Text: dx dx +4 +5x = 1 dt dt?
Answer Preview: The differential equation can be represented in the Laplace domain as s 2 X s 4 s X s 5 X s 1 s Rear…

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, Chapter: 12 -Problem: 11 >> Briefly describe the design technique for an observer, given the configuration you described in Question 9.
Answer Preview: The observer method is a Behavioral design Pattern which allows you to define or create a su…

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, Chapter: 12 -Problem: 5 >> Under what conditions can inspection of the signal-flow graph of a system yield immediate determination of controllability?
Answer Preview: The signal always travels along the branch towards the …

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, Chapter: 2 -Problem: 6 >> What do we call the mechanical equations written in order to evaluate the transfer function?
Answer Preview: In engineering a transfer function also known as system function or network function of a system s…

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, Chapter: 12 -Problem: 39 >> a. Redesign the dc-dc converter system of Problem 36 to include integral control.b. Simulate your system for a step input using Simulink and verify that the specifications are met. In particular, verify that the system has zero steady-state error.
Answer Preview: The failure of DC DC converter would result in the swi…

, Chapter: 3 -Problem: 11 >> For each system shown in Figure P3.9, write the state equations and the output equation for the phase-variable representation. Transcribed Image Text: R(s) 8s + 10 C(s) s4 + 5s + s2 + 5s + 13 (a) R(s) C(s) s4+ 2s3+ 12s2+ 7s +6 55+ 9s4+ 13s3+ 852 (b) FIGURE P3.9
Answer Preview: R S 83 10 S 58 s 55 13 State equation lll Output equation c s c D R S i e Transfer function 8s 10 s …

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, Chapter: 13 -Problem: 1 >> Derive the z-transforms for the time functions listed below. Do not use any z-transform tables. Use the plan f (t) ? f *(t) ? F*(s) ? F(z), followed by converting F(z) into closed form making use of the fact that 1/(1 - z-1) = 1 + z-1 + z-2 + z-3 + ? ? ? . Assume ideal sampling.a. e-atu(t)b. u(t)c. t2e-atu(t)d. cos ?t u(t)
Answer Preview: a F z 1 z 1 b F z …

, Chapter: 8 -Problem: 13 >> Briefly describe how the zeros of the open-loop system affect the root locus and the transient response.
Answer Preview: The zeros of the open loop sys…

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, Chapter: 2 -Problem: 54 >> Consider the differential equationwhere f(x) is the input and is a function of the output, x. If f (x) = 3e-5x, linearize the differential equation for x near 0. Transcribed Image Text: d'x dr + 10+ dx dx + 20+ 15x = f(x) dr dt
Answer Preview: The linearization of the differential equation near x 0 involves finding the Taylor series a…

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, Chapter: 8 -Problem: 34 >> For the unity feedback system shown in Figure 8.3, wheredo the following: [Section: 8.7]a. Find the gain, K, to yield a 1-second peak time if one assumes a second-order approximation.b. Check the accuracy of the second-order approximation using MATLAB to simulate the system. Transcribed Image Text:
Answer Preview: a To find the gain K that yields a 1 second peak time using a second order approximation we need to …

, Chapter: 12 -Problem: 22 >> Repeat Problem20 assuming that the plant is represented in phase-variable form. Do not convert to observer canonical form. Data from Problem 20Consider the plant whose state variables are not available. Design an observer for the observer canonical variables to yield a transient response described by ? = 0.6 and ?n = 50. Place the third pole 10 times farther from the imaginary axis than the domina
Answer Preview: To design an observer for the phase variable form of the plant we need to first express the plant in …

, Chapter: 3 -Problem: 1 >> Give two reasons for modeling systems in state space.
Answer Preview: Two reaosons for modeling system in state space 1 state space model g…

, Chapter: 8 -Problem: 44 >> Letin Figure P8.3.a. Find the range of K for closed-loop stability.b. Plot the root locus for K > 0.c. Plot the root locus for K < 0.d. Assuming a step input, what value of K will result in the smallest attainable settling time?e. Calculate the system’s ess for a unit step input assuming the value of K obtained in Part d.f. Make an approximate hand sketch of the unit step response of the system if
Answer Preview: a To find the range of K for closed loop stability we need to check the Routh Hurwitz stability criterion The characteristic equation of the closed loop system is given by s 2 5 K s 6 K 0 The Routh Hu…

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, Chapter: 8 -Problem: 37 >> For the unity feedback system shown in Figure P8.3, wheredo the following:a. Find the location of the closed-loop dominant poles if the system is operating with 15% overshoot.b. Find the gain for Part a.c. Find all other closed-loop poles.d. Evaluate the accuracy of your second-order approximation. Transcribed Image Text:
Answer Preview: a To achieve 15 overshoot in a closed loop system we need to place the closed loop dominant poles at a damping ratio of 0 5 The damping ratio is given …

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, Chapter: 2 -Problem: 69 >> In a significant number of cases, the open-loop transfer function from fluid flow to fluid temperature in a parabolic trough collector can be approximated (Camacho, 2012) by:a. Write an analytic expression for the unit step response of the open loop system assuming that h(t) represents the output temperature and q(t) the input fluid flow.b. Make a sketch of the unit step response of the open-loop
Answer Preview: a To find the unit step response of the open loop system we can take the Laplace transform of the gi…

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, Chapter: 13 -Problem: 4 >> Of what does the block diagram model for a computer consist?
Answer Preview: Block Diagram of Computer A Block diagram of a com…

, Chapter: 2 -Problem: 21 >> a. Write, but do not solve, the mesh and nodal equations for the network of Figure P2.6.b. Use MATLAB, the Symbolic Math Toolbox, and the equations found in part a to solve for the transfer function, G(s) = Vo(s)/V(s). Use both the mesh and nodal equations and show that either set yields the same transfer function. Transcr
Answer Preview: a Mesh Equation Nodal Equation See this for these equations b Matlab Code syms s V Co…

, Chapter: 8 -Problem: 8 >> The characteristic polynomial of a feedback control system, which is the denominator of the closed-loop transfer function, is given by s3 + 2s2 + (20K + 7)s + 100K. Sketch the root locus for this system.
Answer Preview: The root locus for a feedback control system with a characteristic polynomial of s3 2s2 20K 7 s 100K …

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, Chapter: 2 -Problem: 68 >> Problem 23 in Chapter 1 discusses the cruise control of serial, parallel, and split-power hybrid electric vehicles (HEVs). The functional block diagrams developed for these HEVs indicated that the speed of a vehicle depends upon the balance between the motive forces (developed by the gasoline engine and/or the electric motor) and running resistive forces. The resistive forces include the aerodynam
Answer Preview: a To derive the equation for car acceleration we start with the given equation for surplus force a F Fw km m and substitute the expressions for Fw FRo FL and FSt based on the resistive forces given Fw …

, Chapter: 8 -Problem: 11 >> Describe the conditions that must exist for all closed-loop poles and zeros in order to make a second-order approximation.
Answer Preview: 1 Poles must be at least five t…

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, Chapter: 2 -Problem: 20 >> Repeat Problem 19 using nodal equations.Data From Problem 19:Find the transfer function, G(s) = Vo(s)/Vi(s), for each network shown in Figure P2.5. Solve the problem using mesh analysis. Transcribed Image Text: + V(1)- 1 H 1 H 10 2 H 3 H vi(1) 12 vi(1) 1F Volt) (a) (b) FIGURE P2.5 HE 1/2
Answer Preview: In order to solve the problem using nodal analysis we first need to identify the number of nodes in …

, Chapter: 2 -Problem: 27 >> For the system of Figure P2.12 find the transfer function, G(s) = X1(s)/F(s). Transcribed Image Text: K = 4 N/m -Xj K, = 5 N/m ft) = 3 N-s/mM1 =T'kg Jv2=3N-s/m M2 = 2 kg fva = 2 N-s/m %3D FIGURE P2.12
Answer Preview: G s X1 s M1k…

, Chapter: 12 -Problem: 18 >> If an open-loop plant is represented in parallel form, design a controller to yield a closed-loop response of 20% overshoot and a peak time of 0.2 second. Design the controller by first transforming the plant to controller canonical form. Transcribed Image Text: 100 G(s) = s(s + 4)(s+ 10)
Answer Preview: To design a controller to yield a closed loop response of 20 overshoot and a peak time of 0 2 second…

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, Chapter: 8 -Problem: 8 >> How can you tell from the root locus if the settling time does not change over a region of gain?
Answer Preview: since the root locus is the locus of the closed …

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, Chapter: 13 -Problem: 18 >> Given a point on the z-plane, how can one determine the associated percent overshoot, settling time, and peak time?
Answer Preview: As one increases the proportional gain the system becomes faster but care must be taken not make …

, Chapter: 3 -Problem: 15 >> Use MATLAB to find the transfer function, G(s)=Y(s)/R(s), for each of the following systems represented in state space:a)b) Transcribed Image Text: 01 ?? 1 5 x+ 1 8 -9 -2 -3 2 y = [1 3 6 6]x 1.
Answer Preview: Answer MATLAB Program a clear all clc syms s input the A B C D matrices …

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, Chapter: 8 -Problem: 6 >> For the open-loop pole-zero plot shown in Figure P8.4, sketch the root locus and find the break-in point. Transcribed Image Text: ja s-plane jl -3 -2 -1 -jl FIGURE P8.4
Answer Preview: The Bode plot provides the relative stability of the system in terms of the gain margin and phase …

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, Chapter: 2 -Problem: 6 >> Use MATLAB and the Symbolic Math Toolbox to find the Laplace transform of the following time functions:a. f (t) = 8t2cos (3t + 45°)b. f (t) = 3te-2tsin (4t + 60°)
Answer Preview: answers …

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, Chapter: 12 -Problem: 2 >> Briefly describe the design procedure for a controller.
Answer Preview: Answer The process of designing a control system usually makes many demands of the engineer or engi…

, Chapter: 2 -Problem: 16 >> Use MATLAB and the Symbolic Math Toolbox to input and form LTI objects in polynomial and factored form for the following frequency functions:a.b. Transcribed Image Text: 45(s? + 37s+ 74)(s + 28s? + 32s + 16) (s+ 39)(s+ 47)(s? + 2s+ 100)(s + 27s? + 18s+ 15) Gs) %3D
Answer Preview: For the first frequency function you can use the zpk command in MATLAB to input and form the L…

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, Chapter: 12 -Problem: 19 >> For a spe

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