22Q2A PID controller is designed to control the robot leg, and the control system is shownin Figure 2.(a)Find the transfer function (s)/R(s).(b)R(s)[15 marks]Use the Routh-Hurwitz stability criterion to determine the range of the parameterK such that the closed-loop system is stable.+K2+-+sSPID ControllerFigure 24s² + 3s + 4Robot Leg dynamics[25 marks]℗(s)

Answered: 22 Q2 A PID controller is designed to…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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You are tasked to enhance the performance of an analog plant using a digital controller PID. The controller is in connected in series with the plant in a closed-loop configuration. The pulse transfer K(z+a) function is given as GzohGp(s) =- Use sampling time Ts=0.6 second, K=8, a=0.78, b=-0.602 (0+z)(q+z) and c=-0.705. Do the following: i. Obtain the design point in z-coordinates to achieve the requirement of having a system settling time of 3 second, and damping ratio of zeta (z=0.705).
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Given the system equipped with unitary feedback, whose direct branch transfer function is: Design a PID controller with one of the Ziegler-Nichols methods.
Below is a very common feedback block system. It is a 1dof, and unity-feedback system. The input is the reference command R(s). This is what flows out of thin air, into the system. All other signals in the system (e.g. U, Y, etc.) will depend on R(s). R(s) a. E(s) e. K U(s) G Y(s) Write the algebraic relation between the output Y(s) and the reference R(s) in terms of G and K?. Write it in the format Y = some function of s * R b. What is the TF from R to Y, aka the closed loop TF? What is the "Loop TF" aka the "the open-loop TF"? G has zeros at ZG1, ZG2 etc. and poles at PG1, PG2 etc. C. K has zeros at ZK1, ZK2 etc. and poles at PK1, PK2 etc. What are the zeros and the poles of OLTF? What are the zeros and the poles of CLTF? d. Write the algebraic relation between the error E(s)=R-Y and the reference R(s) in terms of G and K? Write it in the format E = some function of s * R. What is the TF from R to E? Write the algebraic relation between the controller output U(s) and the reference…
The open loop transfer function of a unity feedback control system is given below; G(s) = K s(s+2)(s2+2s+2) Plot the root locus and determine the value of k at the break away point.
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