Engineering

Electrical EngineeringQ&A LibraryExcercise 4: PI control for a first-order plant. Suppose you are to design a feedback controller for afirst-order plant depicted in the figure below:ControllerPlantКkpTS 1SThis configuration is referred to as a proportional-integral (PI) controller. You are to design the controllerto satisfy some given time-domain specifications.(a) Find the (closed-loop) transfer function Gyr from r to y (see hw02).(b) Determine the steady-state error for a unit step input (Hint: e r --y)(c) Find the transfer function Gun from n to u.(d) Determine k, and ki such that the feedback controlled system has damping ratio Ç = 0.5 and fre-quency wo. (Hint: the desired denominator polynomial for a closed-loop transfer function is of theform: d(s) s2+ 2Çwos +w2.)From now on, let K = 1, t = 1.(e) Find the values for kp and ki so that the frequency of the closed-loop system is 1, i.e. wo = 1. Thiscontroller will be referred to as controller 1.(f) Also, find the values for k, and k so that the frequency of the closed-loop system is 0.1, i.e. woThis controller will be referred to as controller 2.= 0.1(g) Analyze the tracking ability of both controller 1 and 2 by simulation in MATLAB. For instance,consider the step response of Gur. What is the input and what the output? Plot the results on oneplot, and include a legend(h) Analyze the ability of the system to reject sensor noise n by plotting the step-response of GunWhat is the input and what the output? Plot the responses of both controller 1 and 2 on one plot.(i) Based on your results, which controller do you think is 'best'?Question

Asked Oct 13, 2019

4 views

Step 1

Hi! Thank you for the question. I am solving the Question for first 3 sub-parts as you have posted the question with multiple sub-parts. Kindly post the remaining sub-parts as separate Question. Thank you.

**Part (a):**

The closed-loop transfer function from *r* to *y* is obtained as follows:

Step 2

From Figure 2, obtain the required closed-loop transfer function from *r* to *y* as follows:

Step 3

**Part (b):**

Write the expression for steady-state erro...

Tagged in

Find answers to questions asked by student like you

Show more Q&A

Q: Airframe Electrical What is the purpose of the inspection hole on a connector contact?

A: There are different kind of connectors. Crimped contacts are mostly used connectors.Connectors are m...

Q: The three conductors of a 3-Φ transmission line are arranged in a horizantal plane and are 5m apart....

A: Consider that the phase inductance of phase conductor R,Y and B are LA, LB and LC respectively, geo...

Q: Can I please get some help with problem 25 I am lost.

A: The given circuit diagram is:

Q: can you please explain what a supernode is, how do I apply it in this question.

A: To find the value of V1 and V2 by super-node concept in the given circuit:

Q: KCL Iav 2N 0sv Soue the curcut gnd

A: The circuit diagram is shown on the board:

Q: A substation receives 6000 kVA at 6 kV, 0.8 p.f. lagging on low voltage side of a transformer from a...

A: The single line diagram of the system is shown below:

Q: In the following circuit, use either differential equation approach or the shortcut method to find i...

A: STEP BY STEP METHOD:From the circuit, write the expression for io(t) as follows:

Q: i1 = 9 A, i2 = -3 A, and v1 = -4 V I need to find Vx using nodal analysis.

A: To find the voltage (Vx) in the given circuit by using nodal analysis.

Q: When the waveform shown in fig. (1) is applied to true responding ac voltmeter, the output would be ...

A: The signal given is applied to average responding AC voltmeter. The indicate value, true value, true...