G(s)=1/(s^2+6s+5)Homework Answers
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****** Matlab Code *******
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% effect of compensators on system stability
h = tf(1,[1 3]);
g = tf(1,[1 6 5]);
dc = tf([1 4],[1 16]);
rlocus(h*g*dc)
****** End of Code ******
Output:
We see that with the lead compensator, the gain at which the root locus crosses the imag axis has increased to 1730, resulting in increased stability for the system
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G(s)=1/(s^2+6s+5)
Unless otherwise stated, the following block diagram (Figure 5.1 from the textbook) is assumed in...
NOTE 2: Initial conditions assumed to be 0 unless otherwise is stated 1) Consider the system depi...
NOTE 2: Initial conditions assumed to be 0 unless otherwise is stated 1) Consider the system depicted below Input: v, Output: vo Assume that c (0)2, v2 (0)0 a) b) c) d) Derive the mathematical model of the system using mesh current method Find unit impulse response Find unit step response Find the transfer function T(s)Vo (s)/V(s) 2) Consider the system depicted below 2,20.5 Input: v, Output: i Assume that i,(0) 1, vc(00 a) Derive the mathematical model of the...
Unless otherwise stated, all objects are located near the Earth's surface, where g = 9.80 m/s^2...
Unless otherwise stated, all objects are located near the
Earth's surface, where g = 9.80 m/s^2 .
In the apparatus shown in the figure (Figure 1) , m1 = 15kg
and the coefficients of static and kinetic friction between
m1 and the table are 0.65 and 0.36, respectively.
a)What mass of m2 will just barely set the system in
motion?
b)After the system begins to move, what is the acceleration?
Unless otherwise stated, all objects are located near the Earth's...
Question 8 1 pts Figure 5.42 Controller Process G (s) Y(s) R(s) G(s) Block diagram for...
Question 8 1 pts Figure 5.42 Controller Process G (s) Y(s) R(s) G(s) Block diagram for the Skills Check. Consider the block diagram of the control system shown in Figure 5.42 in Problems 8 and 9 with the loop transfer function K L(s) G,(s)G(s) s(s+10) Find the value of K so that the system provides an optimum ITAE response. OK= 1.10 K 12.56 K= 51.02 K = 104.7
Question 8 1 pts Figure 5.42 Controller Process G (s) Y(s) R(s)...
03. (a) Consider the block diagram shown in Figure 3.1, and assume G(s)= 3. G,(s) and...
03. (a) Consider the block diagram shown in Figure 3.1, and assume G(s)= 3. G,(s) and G,(s) 5+2 Y(s) R(S) G,() Gy(s) G;(s) Figure 3.1 3 (0) Y(s) Derive the system transfer function H(s)= of the system. Plot the R(s) poles and zeros of H(s) in the complex s-plane. State whether the system is stable or not stable, and why. [10 marks) (11) Obtain the impulse response of the system, that is ylt) for r(t)= 8(t). Evaluate the final value...
1) Use Simulink to plot the unit step response of the following block diagram for K-1, 2, 5 and f...
1) Use Simulink to plot the unit step response of the following block diagram for K-1, 2, 5 and find Mp, tp, ts from the figure. (116s2 +1187s+8260) K(s) K controller plant R(s) K(s) G(s) Y(s) 2) Find the state variable representation of closed loop system of (1) by using Simulink.
1) Use Simulink to plot the unit step response of the following block diagram for K-1, 2, 5 and find Mp, tp, ts from the figure. (116s2 +1187s+8260) K(s)...
C(s) G(s) Figure 1: A block diagram for Problems 1-4 For the given unity feedback system with G(s...
C(s) G(s) Figure 1: A block diagram for Problems 1-4 For the given unity feedback system with G(s) - s 5)3' (a) Find the location of the dominant poles to yield a 1.2 second settling time and overshoot of 15% (b) If a compensator with a zero at-1 is used to achieve the conditions of Part a, what must be the angular contribution of the compensator pole be? (c) Find the location of the compensator pole. (d) Find the gain...
Answer all questions. Unless otherwise stated, all the DFAs and NFAs in this homework use 2-...
Answer all questions. Unless otherwise stated, all the DFAs and NFAs in this homework use 2- 10,1j as the alphabet. 1. (50 point) For i-1,2 and 3, design NFAs Ni, such that L(N) - B5, where: (a) Bi-{w|w has an even number of O's, or, contains exactly two 1's) (b) ) B2- w every odd position of w is 1 (c) B3 - [w| all strings except the empty string and the string 11) (d) B4- [0j with two states....
5. A milling machine has the following open-loop transfer function: (s 1)(s+3) Draw a block diagram describing a negati...
5. A milling machine has the following open-loop transfer function: (s 1)(s+3) Draw a block diagram describing a negative feedback system that includes a plant a) with transfer function of Gi(s) and a cascade proportional controller with a gain of K. b) Write the closed-loop transfer function for such a negative feedback system c The plant has poles that are solutions to P(s) 0 and zeros that are the solutions to Z(s)-0. Write an equation involving K, P(s) and Z(s)...
1. (30 points) The block diagram of a machine-tool control system is shown in Figure 1. (a) (10 p...
1. (30 points) The block diagram of a machine-tool control system is shown in Figure 1. (a) (10 points) Determine the transfer function H(s) = Y(s)/R(s) (b) (10 points) Determine the sensitivity S (c) (10 points) For 1
Problem 2. (40 points) The following figure shows the block diagram of a feedback closed loop...
Problem 2. (40 points) The following figure shows the block diagram of a feedback closed loop control system. Ysp(s) - Es) | U(s) Y(s) S +5 1 Ge(s) Q"46:0) " ** 52_1 (a) Find the range of controller settings that yield stable closed-loop system for: (i) A proportional-only (P) controller. (ii) A proportional-integral (PI) controller. (b) For the PI control, modify the block diagram to eliminate proportional kick.
NOTE 2: Initial conditions assumed to be 0 unless otherwise is stated 1) Consider the system depicted below Input: v, Output: vo Assume that c (0)2, v2 (0)0 a) b) c) d) Derive the mathematical model of the system using mesh current method Find unit impulse response Find unit step response Find the transfer function T(s)Vo (s)/V(s) 2) Consider the system depicted below 2,20.5 Input: v, Output: i Assume that i,(0) 1, vc(00 a) Derive the mathematical model of the...
Unless otherwise stated, all objects are located near the
Earth's surface, where g = 9.80 m/s^2 .
In the apparatus shown in the figure (Figure 1) , m1 = 15kg
and the coefficients of static and kinetic friction between
m1 and the table are 0.65 and 0.36, respectively.
a)What mass of m2 will just barely set the system in
motion?
b)After the system begins to move, what is the acceleration?
Unless otherwise stated, all objects are located near the Earth's...
Question 8 1 pts Figure 5.42 Controller Process G (s) Y(s) R(s) G(s) Block diagram for the Skills Check. Consider the block diagram of the control system shown in Figure 5.42 in Problems 8 and 9 with the loop transfer function K L(s) G,(s)G(s) s(s+10) Find the value of K so that the system provides an optimum ITAE response. OK= 1.10 K 12.56 K= 51.02 K = 104.7
Question 8 1 pts Figure 5.42 Controller Process G (s) Y(s) R(s)...
03. (a) Consider the block diagram shown in Figure 3.1, and assume G(s)= 3. G,(s) and G,(s) 5+2 Y(s) R(S) G,() Gy(s) G;(s) Figure 3.1 3 (0) Y(s) Derive the system transfer function H(s)= of the system. Plot the R(s) poles and zeros of H(s) in the complex s-plane. State whether the system is stable or not stable, and why. [10 marks) (11) Obtain the impulse response of the system, that is ylt) for r(t)= 8(t). Evaluate the final value...
1) Use Simulink to plot the unit step response of the following block diagram for K-1, 2, 5 and find Mp, tp, ts from the figure. (116s2 +1187s+8260) K(s) K controller plant R(s) K(s) G(s) Y(s) 2) Find the state variable representation of closed loop system of (1) by using Simulink.
1) Use Simulink to plot the unit step response of the following block diagram for K-1, 2, 5 and find Mp, tp, ts from the figure. (116s2 +1187s+8260) K(s)...
C(s) G(s) Figure 1: A block diagram for Problems 1-4 For the given unity feedback system with G(s) - s 5)3' (a) Find the location of the dominant poles to yield a 1.2 second settling time and overshoot of 15% (b) If a compensator with a zero at-1 is used to achieve the conditions of Part a, what must be the angular contribution of the compensator pole be? (c) Find the location of the compensator pole. (d) Find the gain...
Answer all questions. Unless otherwise stated, all the DFAs and NFAs in this homework use 2- 10,1j as the alphabet. 1. (50 point) For i-1,2 and 3, design NFAs Ni, such that L(N) - B5, where: (a) Bi-{w|w has an even number of O's, or, contains exactly two 1's) (b) ) B2- w every odd position of w is 1 (c) B3 - [w| all strings except the empty string and the string 11) (d) B4- [0j with two states....
5. A milling machine has the following open-loop transfer function: (s 1)(s+3) Draw a block diagram describing a negative feedback system that includes a plant a) with transfer function of Gi(s) and a cascade proportional controller with a gain of K. b) Write the closed-loop transfer function for such a negative feedback system c The plant has poles that are solutions to P(s) 0 and zeros that are the solutions to Z(s)-0. Write an equation involving K, P(s) and Z(s)...
1. (30 points) The block diagram of a machine-tool control system is shown in Figure 1. (a) (10 points) Determine the transfer function H(s) = Y(s)/R(s) (b) (10 points) Determine the sensitivity S (c) (10 points) For 1
Problem 2. (40 points) The following figure shows the block diagram of a feedback closed loop control system. Ysp(s) - Es) | U(s) Y(s) S +5 1 Ge(s) Q"46:0) " ** 52_1 (a) Find the range of controller settings that yield stable closed-loop system for: (i) A proportional-only (P) controller. (ii) A proportional-integral (PI) controller. (b) For the PI control, modify the block diagram to eliminate proportional kick.
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