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For the Transfer functions listed, determine Ess, if S2 1. G(S) = and input is r(t)...
3. Work the following problems: a. The transfer function of a system is: Y(s)/R(s) = 15(s+1)/(s2+9s+14)....
3. Work the following problems: a. The transfer function of a system is: Y(s)/R(s) = 15(s+1)/(s2+9s+14). Determine y(t) when r(t) is a unit step input. b. Consider the following system: R(s)_ 0 G(s) i. Find the closed-loop transfer function Y(s)R(S) when G(s) = 10/(S2+2s+10) ii. Determine Y(s) when the input R(s) is a unit step. iii. Compute y(t).
11- The unity feedback system has an Ess 1/6000 for an input of 10tu(t). Given: k(s2...
11- The unity feedback system has an Ess 1/6000 for an input of 10tu(t). Given: k(s2 3s 30) s (s 5) Find k and n that satisfies the given specifications.
Letting the input R(s) = 1/s, determine the output, x(t), for the following transfer function: 20...
Letting the input R(s) = 1/s, determine the output, x(t), for the following transfer function: 20 X(s) 20 R(S) – (52 + 25 + 5) – (s +1 +21)(s +1 – 21) Use the following Laplace Transforms: F(s) f(t) 1/s 1 As + o) + BW (s + 5)2 + w2 Ae-ot cos(wt) + B e-ot cos(wt)
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)
1. Consider a feedback system given below: T(s) Disturbance Controller Dynamics R(S) + Gc(s) G.(s) U(s)...
1. Consider a feedback system given below: T(s) Disturbance Controller Dynamics R(S) + Gc(s) G.(s) U(s) Sensor H(s) IMs) Sensor noise where the input and transfer functions are given as follows: R(s) = –,7,(s) = 0, N(s) = 0, G, - 15,6, -_- , and H(s) = 1. s's + 3) a. Derive the system transfer function Y(s)/R(s) = G,, poles, $, On, and, from the response function y(t), the performance measures: rise time Tr, peak time Tp, percent overshoot...
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 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)...
8 The transfer function of a linear time invariant system is given as G(s) = 10/(S2...
8 The transfer function of a linear time invariant system is given as G(s) = 10/(S2 + 10s + 10). The steady state value of the output of the system for step input (R(s) = 1/s^2) will be: DS (3 Points) 100 0.1 O infinity None of them 0.01 1 10
R(s)) C(s) 1. For the unity feedback system shown above where K(s2 +2s +5) G(S)2(s +3)...
R(s)) C(s) 1. For the unity feedback system shown above where K(s2 +2s +5) G(S)2(s +3) a) b) c) Find the system type. What error can be expected for an input of 10u(t)? What error can be expected for an input of 10tu(t)?
Example 3.3.1 A control system shown in following Figure G(s)=(s+1) C(s) N(s) E(s) G,(S) R(s) S...
Example 3.3.1 A control system shown in following Figure G(s)=(s+1) C(s) N(s) E(s) G,(S) R(s) S G2(s) 100 G2(s)= s(s+10) H(s) H(s) 1 1. If n(t) 0, r(t)=5+2t+10t?, make e 0.1, k-? 2. If n(t)=t, r(t)=5+2t+10t2, k=1, e=? sS I ess0.1, k=?. Question14 A control system shown in following Figure, obtain the steady-state error transfer function E(s)/N(s). N(s) E(S) GS C(S) G.(S) R(s) H(s) Question12 Obtain both analytically and computationally the rise time, peak time, maximum overshoot, and settling time...
3. Work the following problems: a. The transfer function of a system is: Y(s)/R(s) = 15(s+1)/(s2+9s+14). Determine y(t) when r(t) is a unit step input. b. Consider the following system: R(s)_ 0 G(s) i. Find the closed-loop transfer function Y(s)R(S) when G(s) = 10/(S2+2s+10) ii. Determine Y(s) when the input R(s) is a unit step. iii. Compute y(t).
11- The unity feedback system has an Ess 1/6000 for an input of 10tu(t). Given: k(s2 3s 30) s (s 5) Find k and n that satisfies the given specifications.
Letting the input R(s) = 1/s, determine the output, x(t), for the following transfer function: 20 X(s) 20 R(S) – (52 + 25 + 5) – (s +1 +21)(s +1 – 21) Use the following Laplace Transforms: F(s) f(t) 1/s 1 As + o) + BW (s + 5)2 + w2 Ae-ot cos(wt) + B e-ot cos(wt)
1. Consider a feedback system given below: T(s) Disturbance Controller Dynamics R(S) + Gc(s) G.(s) U(s) Sensor H(s) IMs) Sensor noise where the input and transfer functions are given as follows: R(s) = –,7,(s) = 0, N(s) = 0, G, - 15,6, -_- , and H(s) = 1. s's + 3) a. Derive the system transfer function Y(s)/R(s) = G,, poles, $, On, and, from the response function y(t), the performance measures: rise time Tr, peak time Tp, percent overshoot...
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 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)...
8 The transfer function of a linear time invariant system is given as G(s) = 10/(S2 + 10s + 10). The steady state value of the output of the system for step input (R(s) = 1/s^2) will be: DS (3 Points) 100 0.1 O infinity None of them 0.01 1 10
R(s)) C(s) 1. For the unity feedback system shown above where K(s2 +2s +5) G(S)2(s +3) a) b) c) Find the system type. What error can be expected for an input of 10u(t)? What error can be expected for an input of 10tu(t)?
Example 3.3.1 A control system shown in following Figure G(s)=(s+1) C(s) N(s) E(s) G,(S) R(s) S G2(s) 100 G2(s)= s(s+10) H(s) H(s) 1 1. If n(t) 0, r(t)=5+2t+10t?, make e 0.1, k-? 2. If n(t)=t, r(t)=5+2t+10t2, k=1, e=? sS I ess0.1, k=?. Question14 A control system shown in following Figure, obtain the steady-state error transfer function E(s)/N(s). N(s) E(S) GS C(S) G.(S) R(s) H(s) Question12 Obtain both analytically and computationally the rise time, peak time, maximum overshoot, and settling time...
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