Question:
given a differential equation:
a. initial conditions for the plan and input are zero, derive plan's transfer function in Laplace transform
b. using inverse Laplace transform, find the solution for the differential equation for the plan (find function y(t)).
c. derive state-space model of the plan
d. Assume open-loop system with no controller added to the plant, analyse the steady-state value of the system using final value theorem and step input
e. Calculate value of the overshoot, rise time and setting time for the plant.
f. closed loop added to the plant:
G1 is the plant transfer function, determin value of steady-state error to the step input function
g. Derive transfer function for the closed loop system
h.from the transfer function get from g. , calculate value of Ki, which give 10% overshoot, when the step input is applied.
i. Plot bode plot for the open-loop system, consist of plant only
j. Plot bode plot for the closed-loop system, with Ki=55, consist of plant only
Please help me with this exercise, thank you
rft) K/s yit)
Homework Answers
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Question: given a differential equation: a. initial conditions for the plan and input are zero, ...
Spring 2019 3. Given a closed-loop control system with unity feedback is shown in the block...
Spring 2019 3. Given a closed-loop control system with unity feedback is shown in the block diagram. G(s) is the open-loop transfer function, and the controller is a gain, K. 1. (20) Calculate the open-loop transfer function tar →Q--t G(s) (10) Calculate the steady-state error to a step input of the open-loop system. 7. (in Bode Form) from the Bode plot. (10) Calculate the shortest possible settling time with a percentage overshoot of 5% or less. 8. 2. (10)Plot the...
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Answer all parts and show all work.
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A unity feedback system with the forward transfer function G)2)(s +5) is operating with a closed-loop step response that has 15% overshoot. Do the following: a) Evaluate the settling time for a unit step input; b) Design a PD control to yield a 15% overshoot but with a threefold reduction in settling time; c) Evaluate the settling time, overshoot, and steady-state error with the PD control.
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Spring 2019 3. Given a closed-loop control system with unity feedback is shown in the block diagram. G(s) is the open-loop transfer function, and the controller is a gain, K. 1. (20) Calculate the open-loop transfer function tar →Q--t G(s) (10) Calculate the steady-state error to a step input of the open-loop system. 7. (in Bode Form) from the Bode plot. (10) Calculate the shortest possible settling time with a percentage overshoot of 5% or less. 8. 2. (10)Plot the...
1 T I т I N F The transfer function of a linear differential equation is defined by the Laplace transform of output (response function) over the Laplace transform of input (driving force) The block diagram of a system is not unique. F In the system with the first order differential equation, the steady-state error due to unite step function is not zero. F In a system with a sinusoidal input, the response at the steady state is sinusoidal at...
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 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)...
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Answer all parts and show all work.
Design a Pl or PDcontroller for the system Go)+ 10 to meet the following specifications Zero steady state error for unit step reference input ·4 < 0.12s . %OS < 10%. (a) Determine the low frequency gain, crossover frequency and phase margin necessary to meet the (b) Decide if C() needs an integrator. Plot the Bode plot of either G(s) or G(o)/s, depending on (c) Use sisotool (or iteration) to choose a gain...
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please solve as matlab code.
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