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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...
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 feedback sy PID COntroller Plant R(S) Y(s) the closed-loop transfer function T(s) = Y...
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.
Wis) R(s u(s) 14 Gl(s) H(s) Given a system as in the diagram above, where K is an adjustable pa...
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 the unity-feedback system shown below: R(s) E(s) input: r(t), output: y(t) C(s) P(s) error: e()...
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)...
4. Consider the following closed-loop system in which G(s) = and H(s) = 1. de)_ GC)...
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)
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 fun...
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...
A system with input r(t) and output y(t) has transfer function G(s) = 10 (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) Dev...
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...
Consider the unity feedback system is given below R(S) C(s) G(s) with transfer function: G() =...
Consider the unity feedback system is given below R(S) C(s) G(s) with transfer function: G() = K(+2) s(s+ 1/s + 3)(+5) a) Sketch the root locus. Clearly indicate any asymptotes. b) Find the value of the gain K, that will make the system marginally stable. c) Find the value of the gain K, for which the closed-loop transfer function will have a pole on the real axis at (-0.5).
An automatic feedback control system is shown below. G(o), H(o), and Gc(o) are such that G(s) H(s) = +1 1 = unction Gcu(s) relating Y(9) to R(s) (b) What is the system order? (c) If Tp(s) = 0, in...
An automatic feedback control system is shown below. G(o), H(o), and Gc(o) are such that G(s) H(s) = +1 1 = unction Gcu(s) relating Y(9) to R(s) (b) What is the system order? (c) If Tp(s) = 0, in terms of K and τ determine what value(s) of K, (if any) will result in an undamped closed-loop system Td (s) Y (s) PID R(s) Gc (s) Plant G(s) Sensor H(s)
An automatic feedback control system is shown below. G(o), H(o),...
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 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.
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 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)...
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)
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...
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...
Consider the unity feedback system is given below R(S) C(s) G(s) with transfer function: G() = K(+2) s(s+ 1/s + 3)(+5) a) Sketch the root locus. Clearly indicate any asymptotes. b) Find the value of the gain K, that will make the system marginally stable. c) Find the value of the gain K, for which the closed-loop transfer function will have a pole on the real axis at (-0.5).
An automatic feedback control system is shown below. G(o), H(o), and Gc(o) are such that G(s) H(s) = +1 1 = unction Gcu(s) relating Y(9) to R(s) (b) What is the system order? (c) If Tp(s) = 0, in terms of K and τ determine what value(s) of K, (if any) will result in an undamped closed-loop system Td (s) Y (s) PID R(s) Gc (s) Plant G(s) Sensor H(s)
An automatic feedback control system is shown below. G(o), H(o),...
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