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For the system shown in Fig Q2. Determine the output c(t) when r(t) is: 2. (10...
6.7 For the control system shown in Fig. P6.7, determine the percentage overshoot to a step...
6.7 For the control system shown in Fig. P6.7, determine the percentage overshoot to a step input. Sketch the unit step response of c(t), and estimate the percentage overshoot. 1 + 0.55 0.2 Fig. P6.7
Consider second order system Ce()+250 C( ) + 0Ct) - oR(t ) where R(t) is the system input, C(t) the system response, r...
Consider second order system Ce()+250 C( ) + 0Ct) - oR(t ) where R(t) is the system input, C(t) the system response, r time, damping factor, and o, undamped natural frequency Deduce analytically the condition under which the system will experience over damping, critical damping and underdamping response for a unit step input. b. Using your result in Q4 (a), sketch the graph of the system response with respect to time on each type of response. c. Consider in a...
1. Consider the unity feedback system shown in figure 1 with G(S) -2sti a) Determine the...
1. Consider the unity feedback system shown in figure 1 with G(S) -2sti a) Determine the closed loop transfer function TF(s) γ(s) R(s) What are the poles and zeros of TF1(s)? [2 marks] b) For TF(s), calculate the DC gain, natural frequency and damping ratio. Classify TF1(s) as underdamped overdamped, critically damped or undamped [3 marks] c) Use the initial value theorem and final value theorem to determine the initial value (Mo) and final value (M) of the [2 marks]...
6, Fig. 4 shows three systems. System 1 is a positional servo system. System Π is a positional servo system with PD con...
6, Fig. 4 shows three systems. System 1 is a positional servo system. System Π is a positional servo system with PD control action. System III is a positional servo system with velocity feedback. Compare the unit-step, unit-impulse, and unit-ramp responses of the three systems by using MATLAB. Which system is best with respect to the speed of response and maximum overshoot in the step response? R(s) C(s) #5s + 1) System I R(s) CI(s S1 +0.8)6-D) System II R(s)...
Q.4 A position control system is shown in Figure Q4. Assume that K(s) = K, the plant 50 s(0.2s +1) transfer function is given by G(s) s02s y(t) r(t) Figure Q4: Feedback control system. (a) Design a l...
Q.4 A position control system is shown in Figure Q4. Assume that K(s) = K, the plant 50 s(0.2s +1) transfer function is given by G(s) s02s y(t) r(t) Figure Q4: Feedback control system. (a) Design a lead compensator so that the closed-loop system satisfies the following specifications (i) The steady-state error to a unit-ramp input is less than 1/200 (ii) The unit-step response has an overshoot of less than 16% Ts +1 Hint: Compensator, Dc(s)=aTs+ 1, wm-T (18 marks)...
0.12S [10 marks] 1(e) Determine the input to the system when the output of the system is [10 marks] 1(f) It is required to adjust the gain and the feedback of the states in the companion form state-...
0.12S [10 marks] 1(e) Determine the input to the system when the output of the system is [10 marks] 1(f) It is required to adjust the gain and the feedback of the states in the companion form state-space representation so that the impulse response of the new system with the adjusted gain and feedback is (i) Determine the required transfer function of the new system (i) Form the companion form state-space representation for the new (ii) From the results in...
2. (30 marks] Consider the system shown in Fig. 1. Find the output y(t) for the...
2. (30 marks] Consider the system shown in Fig. 1. Find the output y(t) for the following h(t) and r(t) using the convolution integral. x(r) y(r) h(t) Figure 1: System for Q2 1.5 2t33 0 otherwise h(t)=2rect(-3.5) x(t) = h(t) = 2 rect (-3 -
1. [25%] Consider the closed-loop system shown where it is desired to stabilize the system with...
1. [25%] Consider the closed-loop system shown where it is desired to stabilize the system with feedback where the control law is a form of a PID controller. Design using the Root Locus Method such that the: a. percent overshoot is less than 10% for a unit step b. settling time is less than 4 seconds, c. steady-state absolute error (not percent error) due to a unit ramp input (r=t) is less than 1. d. Note: The actuator u(t) saturates...
4) a) Simplify and then find the transfer function of the system shown in Fig. 2;...
4) a) Simplify and then find the transfer function of the system shown in Fig. 2; b) Determine the position, velocity and acceleration error constants for the transfer function to be found in a) to the unit step, unit ramp and unit parabolic inputs; c) Model the system given in Fig. 2 by Mat Lab/Simulink if it is possible and plot the output variable to the unit step and ramp functions Fig. 2
Question 2 Consider the system shown in Figure Q2, where Wis a unit step disturbance and R is a unit step input. 0.4 s+ 1 10 Figure Q2 (5 marks) (3 marks) (c) Find the value for K so that the steady...
Question 2 Consider the system shown in Figure Q2, where Wis a unit step disturbance and R is a unit step input. 0.4 s+ 1 10 Figure Q2 (5 marks) (3 marks) (c) Find the value for K so that the steady state error due to w(t) is less than 0.01; 6 marks) (d) In order to eliminate the steady state error, show whether a PI controller can be successful 6 marks) (a) Find the expression of E(s)-R(s)-Y(s) in terms...
6.7 For the control system shown in Fig. P6.7, determine the percentage overshoot to a step input. Sketch the unit step response of c(t), and estimate the percentage overshoot. 1 + 0.55 0.2 Fig. P6.7
Consider second order system Ce()+250 C( ) + 0Ct) - oR(t ) where R(t) is the system input, C(t) the system response, r time, damping factor, and o, undamped natural frequency Deduce analytically the condition under which the system will experience over damping, critical damping and underdamping response for a unit step input. b. Using your result in Q4 (a), sketch the graph of the system response with respect to time on each type of response. c. Consider in a...
1. Consider the unity feedback system shown in figure 1 with G(S) -2sti a) Determine the closed loop transfer function TF(s) γ(s) R(s) What are the poles and zeros of TF1(s)? [2 marks] b) For TF(s), calculate the DC gain, natural frequency and damping ratio. Classify TF1(s) as underdamped overdamped, critically damped or undamped [3 marks] c) Use the initial value theorem and final value theorem to determine the initial value (Mo) and final value (M) of the [2 marks]...
6, Fig. 4 shows three systems. System 1 is a positional servo system. System Π is a positional servo system with PD control action. System III is a positional servo system with velocity feedback. Compare the unit-step, unit-impulse, and unit-ramp responses of the three systems by using MATLAB. Which system is best with respect to the speed of response and maximum overshoot in the step response? R(s) C(s) #5s + 1) System I R(s) CI(s S1 +0.8)6-D) System II R(s)...
Q.4 A position control system is shown in Figure Q4. Assume that K(s) = K, the plant 50 s(0.2s +1) transfer function is given by G(s) s02s y(t) r(t) Figure Q4: Feedback control system. (a) Design a lead compensator so that the closed-loop system satisfies the following specifications (i) The steady-state error to a unit-ramp input is less than 1/200 (ii) The unit-step response has an overshoot of less than 16% Ts +1 Hint: Compensator, Dc(s)=aTs+ 1, wm-T (18 marks)...
0.12S [10 marks] 1(e) Determine the input to the system when the output of the system is [10 marks] 1(f) It is required to adjust the gain and the feedback of the states in the companion form state-space representation so that the impulse response of the new system with the adjusted gain and feedback is (i) Determine the required transfer function of the new system (i) Form the companion form state-space representation for the new (ii) From the results in...
2. (30 marks] Consider the system shown in Fig. 1. Find the output y(t) for the following h(t) and r(t) using the convolution integral. x(r) y(r) h(t) Figure 1: System for Q2 1.5 2t33 0 otherwise h(t)=2rect(-3.5) x(t) = h(t) = 2 rect (-3 -
1. [25%] Consider the closed-loop system shown where it is desired to stabilize the system with feedback where the control law is a form of a PID controller. Design using the Root Locus Method such that the: a. percent overshoot is less than 10% for a unit step b. settling time is less than 4 seconds, c. steady-state absolute error (not percent error) due to a unit ramp input (r=t) is less than 1. d. Note: The actuator u(t) saturates...
4) a) Simplify and then find the transfer function of the system shown in Fig. 2; b) Determine the position, velocity and acceleration error constants for the transfer function to be found in a) to the unit step, unit ramp and unit parabolic inputs; c) Model the system given in Fig. 2 by Mat Lab/Simulink if it is possible and plot the output variable to the unit step and ramp functions Fig. 2
Question 2 Consider the system shown in Figure Q2, where Wis a unit step disturbance and R is a unit step input. 0.4 s+ 1 10 Figure Q2 (5 marks) (3 marks) (c) Find the value for K so that the steady state error due to w(t) is less than 0.01; 6 marks) (d) In order to eliminate the steady state error, show whether a PI controller can be successful 6 marks) (a) Find the expression of E(s)-R(s)-Y(s) in terms...
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