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1. Consider a feedback system given below: T(s) Disturbance Controller Dynamics R(S) + Gc(s) G.(s) U(s)...
Q4. The feedback system shown below has a plant, a controller, and sensor transfer functions as G(s), Gc(s) and H(s), respectively. Find the output Y(s) and the input U(s) as a function of the inputs and transfer functions. (2 Points) D(s) R(s) + U(s) Gc (s) O G(s) - Y(s) H(S)
Consider the unity-feedback system shown below: R(s) E(s) input: r(t), output: y(t) C(s) P(s) error: e() r(t) y(t) closed-loop transfer-function: Hyr(sD t the closed-loop transfer-function be Hyr(s) Y (s) R(s) Let the transfer-function of the plant be P(s) 10 s (s 1) (s 5) The open-loop transfer-function is G(s) P(s) C(s) DESIGN OBJECTIVES: Find a controller C(s) such that the following are satisfied i) The closed-loop system is stable. ii) The steady-state error ess due to a unit-ramp input r(t)...
Consider the feedback sy PID COntroller Plant R(S) Y(s) the closed-loop transfer function T(s) = Y controller (Kp Find er p 1, Ks K ) and show that the system is marginally stable with two imaginary roots. (s)/R(s) with no sabl thosed-loop transfer function T(s) Y (S/R(s) with the (three- term) PID controller added to stabilize the system. suming that Kd 4 and K, -100, find the values (range) of Kp that will stabilize the system.
Consider the automobile cruise-control system shown below: Engine ActuatorCarburetor 0.833 and load 40 3s +1 Compensator R(s)E(s) Ge(s) s +1 -t e(t) Sensor 0.03 1) Derive the closed-loop transfer function of V(s)/R(s) when Gc(s)-1 2) Derive the closed-loop transfer function of E(s)/R(s) when Ge(s)-1 3) Plot the time history of the error e(t) of the closed-loop system when r(t) is a unit step input. 4) Plot the root-loci of the uncompensated system (when Gc(s)-1). Mark the closed-loop complex poles on...
Wis) R(s u(s) 14 Gl(s) H(s) Given a system as in the diagram above, where K is an adjustable parameter pl(s) Dal(sKp+ g) Assuming W-0, find the transfer function Y(s)/R(s) h) Assuming R-0, find the transfer function Y(s)/W(s) i) What is the type of the system (with respect to steady-state error)? j) What is the steady-state error when rt)u(t) (unit-step) and w(t)-0 k) What is the s.s. error when r(t) t u(t) and w(t)-0 ) Assume r(t)-0, what is the...
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...
y(s) 2 u(s) s1 -. Consider the open-loop unstable system G(s) integral controller to regulate the output y to a constant reference r. The desired closed-loop transfer function is G) +16s +100 Design the simplest output feedback (20 pts) y(s) 2 u(s) s1 -. Consider the open-loop unstable system G(s) integral controller to regulate the output y to a constant reference r. The desired closed-loop transfer function is G) +16s +100 Design the simplest output feedback (20 pts)
4. Consider the following closed-loop system in which G(s) = and H(s) = 1. de)_ GC) ylt) Derive the transfer function刽 2, where E (s) = R(s) H(s)Y(s). What is the smallest value of K for which the steady-state error due to a unit step disturbance, d(t) -), s less than 0.05? Ea(s) D(s)
A system with input r(t) and output y(t) has transfer function G(s) = 10 (s + 1)(s + 2). Find y(t) for t ≥ 0 if the following inputs are applied (with zero initial conditions): (a) r(t) = u(t) (b) r(t) = e^ −t*u(t)
Problem 1 Given the transfer function from input u(t) to output y(t), s2-4s +3 Y(s) U(s) (s2 + 6s + 8)(82 + 25) (a) Develop a state space model for this transfer function, in the standard form y=Cx + Du (b) Suppose that zero input is applied, such that u 0. Perform a modal analysis of the state response for this open-loop system. Your analysis should include the nature of the time response for each mode, as well as how...