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4 + 3 + 2 = 9 marks) Consider a system with transfer function G(s) 6...
Question 2 20 Marks Consider the transfer function, (6-1)(8-2) (82 7s 12)(s +13) G(s) = 1. Using direct synthesis, synthesize a biproper controller with integral action for this process The desired complementary sensitivity function is given by: (T(s)d- where r is a positive integer to be specified in the design, η1 and η2 are constants to be assigned. 2. What will be the dominant feature of the closed-loop response of the output to a step change in the set-point? Justify...
A unity feedback system with the forward transfer function G(s)=K/(s+1)(s+3)(s+6) is operating with a closed-loop step response that has 15% overshoot. Do the following: a) Evaluate the steady-state error for a unit step input b) Design a PI control to reduce the steady-state error to zero without affecting its transient response c) Evaluate the steady-state error and overshoot for a unit step input to your compensated system A unity feedback system with the forward transfer function G(s) is operating with...
Consider the transfer function of a DC motor given by G(s) = 1 / s(s+2) 3. Consider the transfer function of a DC motor given by 1 G(s) s (s2) The objective of this question is to consider the problem of control design for this DC motor, with the feedback control architecture shown in the figure below d(t r(t) e(t) e(t) C(s) G(s) Figure 4: A feedback control system (a) Find the magnitude and the phase of the frequency response...
The transfer function of a linear system is G(s) = Y(s) S-1 U(s) 5? + 4s +3 a. Express this system in the modal form. b. Express this system in the standard controllable form (SCF). (Parts d, e, f, and g use this system) c. In the standard controllable form, suppose the output is replaced by y=[-1 a] | [x2] Give a value for a which makes the system unobservable. d. What is y(t) if y(0-)=-3, ay = 6 and...
uestionI. A system is represented by the following transfer function G(s)- (s+1)/(s2+5s+6) 1) Find a state equation and state transition matrices (A,B, C and D) of the system for a step input 6u(t). ii) Find the state transition matrix eAt) ii) Find the output response of system y(t) to a step input 6u(t) using state transition matrix, iv) Obtain the output response y(t) of the system with two other methods for step input óu(t). Question IV. A system is described...
4. Consider the transfer function, Y(s)_ 3 F(s) + s(s2 + 2s + 4) (a) Qualitatively, what is the time response y(t) if f(t) represents a unit-step input? What is the value of y(t) when time is sufficiently large? What is the time constant that we may use to evaluate the "speed" of response? (b) Repeat step (a) if f(t) represents an impulse input. What is y(t) when time is sufficiently large?
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...
4. Consider the transfer function, Y($) F(S) 3 S(52 +2s + 4) (a) Qualitatively, what is the time response y(t) if f(t) represents a unit-step input? What is the value of y(t) when time is sufficiently large? What is the time constant that we may use to evaluate the "speed" of response? (b) Repeat step (a) if f(t) represents an impulse input. What is y(t) when time is sufficiently large?
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 (25 points): Consider the open loop system that has the following transfer function 1 G(S) = 10s+ 35 Using Matlab: a) Plot the step response of the open loop system and note the settling time and steady state 15 pts error. b) Add proportional control K 300 and simulate the step response of the closed loop 15 pts system. Note the settling time, %OS and steady state error. c) Add proportional derivate control Kp 300, Ko 10 and...