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Question 8 1 pts Figure 5.42 Controller Process G (s) Y(s) R(s) G(s) Block diagram for...
C(8) for the system shown in Figure 1. R(S Find the equivalent transfer function, Geg (s)...
C(8) for the system shown in Figure 1. R(S Find the equivalent transfer function, Geg (s) 1 Cix) Figure 1. Block diagram 2s+1 s(5s+6Ge(s) = and Figure 2 shows a closed-loop transfer function, where G(s) 2. proper H(s) K+s. Find the overall closed-loop transfer function and express is as rational function. C(s) Ea (s) Controller R(s) +/ Plant G(s) Ge (s) Feedback H(s) Figure 2. Closed loop transfer function Construct the actuation Error Transfer Function associated with the system shown...
Q2. Fig Q2 shows the block diagram of an unstable system with transfer function G(s) -...
Q2. Fig Q2 shows the block diagram of an unstable system with transfer function G(s) - under the control of a lead compensator (a) Using the Routh's stability criterion, determine the conditions on k and a so that the closed-loop system is stable, and sketch the region on the (k, a)- plane where the conditions are satisfied. Hence, determine the minimum value of k for the lead compensator to be a feasible stabilizing controller. (10 marks) (b) Suppose α-2. Given...
Problem 4) (20 Pts.) A Proportional controller is simply a gain block. In figure below, it...
Problem 4) (20 Pts.) A Proportional controller is simply a gain block. In figure below, it is the block with gain 2nd order underdamped plant as shown. Kc which is behind the a) Simplify below block diagram to obtain the overall feedback system transfer funion)R(G) b) Choose Kc so that the overall feedback system transfer function G(s) has 50% overshoot due to a step input (called quarter decay ratio tuning) d) The feedback system transfer function Gs)- is faster than...
Question 6 The open-loop transfer function G(s) of a control system is given as G(8)- s(s+2)(s +5...
Question 6 The open-loop transfer function G(s) of a control system is given as G(8)- s(s+2)(s +5) A proportional controller is used to control the system as shown in Figure 6 below: Y(s) R(s) + G(s) Figure 6: A control system with a proportional controller a) Assume Hp(s) is a proportional controller with the transfer function H,(s) kp. Determine, using the Routh-Hurwitz Stability Criterion, the value of kp for which the closed-loop system in Figure 6 is marginally stable. (6...
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...
Consider a unity-feedback control system with a PI controller Gpr(s) and a plant G(s) in cascade. In particular, the plant transfer function is given as 2. G(s) = s+4, and the PI controller trans...
Consider a unity-feedback control system with a PI controller Gpr(s) and a plant G(s) in cascade. In particular, the plant transfer function is given as 2. G(s) = s+4, and the PI controller transfer function is of the forrm KI p and Ki are the proportional and integral controller gains, respectively where K Design numerical values for Kp and Ki such that the closed-loop control system has a step- response settling time T, 0.5 seconds with a damping ratio of...
Question 4 A control system is shown in Figure 3, where Ge(s) is the controller, R(s)...
Question 4 A control system is shown in Figure 3, where Ge(s) is the controller, R(s) is the setpoint temperature, Tw is the measured water temperature, Ta is the ambient temperature and u(t) is the rate of heat supplied to the heater. The mathematical model of a simple thermal system consisting of an insulated tank of water is given by: dTW = c(1, - Iw) +u dt where c is the heat insulation coefficient. Heater Water R(s) Ta Gc/s) u(1)...
A unity feedback system is described by the block diagram below: R(S) C(s) + G(S) It's...
A unity feedback system is described by the block diagram below: R(S) C(s) + G(S) It's the transfer function, G(s) is given as follows: G(S) = -K(s + 1)? 52 + 25 + 2 Considering that K can have only positive values, the system will be unstable when the value of Kis: OK>2 OK<1 1<K< 2. The correct answer is not listed OK>1 OK<2
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)...
Question 1 (60 points) Consider the following block diagram where G(s)- Controller R(s) G(s) (a) Sketch the root locus assuming a proportional controller is used. [25 points] (b) Design specifica...
Question 1 (60 points) Consider the following block diagram where G(s)- Controller R(s) G(s) (a) Sketch the root locus assuming a proportional controller is used. [25 points] (b) Design specifications require a closed-loop pole at (-3+j1). Design a lead compensator to make sure the root locus goes through this point. For the design, pick the pole of the compensator at-23 and analytically find its zero. (Hint: Lead compensator transfer function will be Ge (s)$+23 First plot the poles and zeros...
C(8) for the system shown in Figure 1. R(S Find the equivalent transfer function, Geg (s) 1 Cix) Figure 1. Block diagram 2s+1 s(5s+6Ge(s) = and Figure 2 shows a closed-loop transfer function, where G(s) 2. proper H(s) K+s. Find the overall closed-loop transfer function and express is as rational function. C(s) Ea (s) Controller R(s) +/ Plant G(s) Ge (s) Feedback H(s) Figure 2. Closed loop transfer function Construct the actuation Error Transfer Function associated with the system shown...
Q2. Fig Q2 shows the block diagram of an unstable system with transfer function G(s) - under the control of a lead compensator (a) Using the Routh's stability criterion, determine the conditions on k and a so that the closed-loop system is stable, and sketch the region on the (k, a)- plane where the conditions are satisfied. Hence, determine the minimum value of k for the lead compensator to be a feasible stabilizing controller. (10 marks) (b) Suppose α-2. Given...
Problem 4) (20 Pts.) A Proportional controller is simply a gain block. In figure below, it is the block with gain 2nd order underdamped plant as shown. Kc which is behind the a) Simplify below block diagram to obtain the overall feedback system transfer funion)R(G) b) Choose Kc so that the overall feedback system transfer function G(s) has 50% overshoot due to a step input (called quarter decay ratio tuning) d) The feedback system transfer function Gs)- is faster than...
Question 6 The open-loop transfer function G(s) of a control system is given as G(8)- s(s+2)(s +5) A proportional controller is used to control the system as shown in Figure 6 below: Y(s) R(s) + G(s) Figure 6: A control system with a proportional controller a) Assume Hp(s) is a proportional controller with the transfer function H,(s) kp. Determine, using the Routh-Hurwitz Stability Criterion, the value of kp for which the closed-loop system in Figure 6 is marginally stable. (6...
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...
Consider a unity-feedback control system with a PI controller Gpr(s) and a plant G(s) in cascade. In particular, the plant transfer function is given as 2. G(s) = s+4, and the PI controller transfer function is of the forrm KI p and Ki are the proportional and integral controller gains, respectively where K Design numerical values for Kp and Ki such that the closed-loop control system has a step- response settling time T, 0.5 seconds with a damping ratio of...
Question 4 A control system is shown in Figure 3, where Ge(s) is the controller, R(s) is the setpoint temperature, Tw is the measured water temperature, Ta is the ambient temperature and u(t) is the rate of heat supplied to the heater. The mathematical model of a simple thermal system consisting of an insulated tank of water is given by: dTW = c(1, - Iw) +u dt where c is the heat insulation coefficient. Heater Water R(s) Ta Gc/s) u(1)...
A unity feedback system is described by the block diagram below: R(S) C(s) + G(S) It's the transfer function, G(s) is given as follows: G(S) = -K(s + 1)? 52 + 25 + 2 Considering that K can have only positive values, the system will be unstable when the value of Kis: OK>2 OK<1 1<K< 2. The correct answer is not listed OK>1 OK<2
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)...
Question 1 (60 points) Consider the following block diagram where G(s)- Controller R(s) G(s) (a) Sketch the root locus assuming a proportional controller is used. [25 points] (b) Design specifications require a closed-loop pole at (-3+j1). Design a lead compensator to make sure the root locus goes through this point. For the design, pick the pole of the compensator at-23 and analytically find its zero. (Hint: Lead compensator transfer function will be Ge (s)$+23 First plot the poles and zeros...
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