Consider a system described by the following differential equation:ÿ – 2ý + y = 2uwhere y and u are the output and input, respectively.(a) Derive a transfer function of the system(b) Check the stability of the system(c) Design a suitable controller for the system so that the closed-loop system is stable, and the output tracksa step reference input. Use MATLAB to simulate and plot the response of the closed-loop system to aunit-step reference input. Does the output now track the reference unit-step input? Show your fullworking including all codes and plots from MATLAB.

Answered: Image /qna-images/answer/92abb19f-40da-44f4-90a2-dadeb3d758c8.jpg

Answered: Consider a system described by the…

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

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control systems In the electromechanical system given below, it can be seen that the coil can be represented by the series R-L circuit and also the coil It is known that the electromagnetic pulling force (F) is also proportional to the coil current, that is, F = βi. The input of the system is the voltage v applied to the coil and the output is the x path taken by the core. Accordingly, the system find the differential equations and transfer function
The control system manages, commands, directs, or regulates the behavior of other devices or systems using control loops. State the advantages of implementing negative feedback in a closed-loop system. Then Write the corresponding differential equation for the transfer function given, Specify the assumption made for the solution.
Consider the mechanical system shown; m is the mass of the body, bis the damping coefficient, k is the stiffness of the spring and F is the applied force. 1) Write the differential equation for the system 2) consifer the force, F, is the input and the displacement of the body of mass, m, is the output of the system. White the transfer function for the system. 3) A proportional controller Kp is applied. Draw the closed loop block diagram for the system. 4)Write the closed loop transfer function for the system with controller Kp.
A car was ignited & a signal from the engine i.e a(z) was passed through a cascade of 2 passive RC lowpass filters to generate an output signal, b(z).a.Show a differential equation derivation to describe the systemb.Make a sketch utilizing circuit diagramc.Mention if the RC system in question above isi.Time in-variant / Time variant ii.Non linear / lineariii.Non-invertible / Invertibleiv. Non-causal / Causal v. Have no memory / Have memory sytems.d. d2b(z)/dz2 + 3(db(z)/dz) +2b(z) = 3(da(z)/dz) +2a(z)Let's assume that the d.e(differential equation) above is that which is characterised by the RC system in the main question above.Where a(z) & b(z) is the input & output of the RC system respectively.Considering an impulse of a(z)=δ(z) is applied to the system, determine the output b(z) of the system
CONTROL SYSTEMA negative unity-feedback control system has the forward path transfer function given as G (s)=(K/S^3+15s^2+50s)a) Draw the root locus diagram.b) Find the K value/value range that makes the system response overdamped.c) Find the K value/value range that makes the system response under damped.d) Find the K value/value range that makes the system response criticully damped.
A hard disk drive (HDD) is an electro-mechanical data storage device that stores and retrieves digital data using magnetic storage and one or more rigid rapidly rotating platters coated with magnetic material. Figure 1 shows a simplified block diagram of a HDD. For analysis purposes, given gain K=30 and G(s)=1 / s(s+4) determine the open-loop and closed loop poles of the HDD and plot these separately in the S-Plane. Also discuss the stability using two different approaches.
The previous solutions are posted on screenshot. please refer to them for gain value. solve : An integrator is added to the PD controller, leading to a PID controller C(s) = kp +ki/s + kds. Keep the PD controllers gains kp and kd from above, and plot the closed-loop poles as the gain ki varies from 0 ! 1 (Hint: The closed-loop poles satisfy 1 + P (s)C(s) = 0, translate this to Evan’s form 1 + kiG(s) = 0). Determine gains such that a load disturbance is rejected in about 10 time units, while keeping the amount of overshoot (from r to y) under 20%. Why can ki not be too large?
A feedback control system is illustrated in Fig. 2. The plant, compensator and sensor transfer functions are given by Gp(s) =5/( 0.2s+1’) Gc(s) = 10, H(s) = 1 Plant RG). a) Write the differential equation of plant Gp(s). This equation relates c(t) and m(t). b) Find closed-loop transfer function C(s)/R(s). c) Find transfer function E(s)/R(s). d) If R(s) is the unit step, find steady-state output Css.
The loop gain GH of a closed loop system is given by the following expression K/s(s+2)(s+4), The value of K for which the system just become unstable is ?
A control system has a closed loop T.F. with unity feedback asY(s)U(s) = K(s + 3)s(s + 2) + K(s + 3)draw the R.L. and design the system to have a damping ratio of 0.866, then find the location of roots.
Ex. 449. K*G(s)=K*1/(s(s+3)(s+6)) is the FTF of a unity-feedback closed-loop system. Calculate the asymptote centroid and show it on a professional root locus plot. Draw the asymptote plot separately. Determine the break-away point and K at the break-away point and show both on the plots. Formal documentation required. ans: 3
Electrical Engineering For a unit feedback system having the following gain functions: G(s) Ks - 4.21) s² (2 s +5.7) 2 (1) Draw the root trajectory. (2) Find the value of the gain K in which all three roots are real and have intermediate roots. (3) When it becomes as in (2), find the value of its root. -thanks you very much for the help ~~

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