s+3Problem 8. For the PD controlled positioning system, where Ge(s) = K(s + 2) and G,(s) :s(s+1)(a) Plot the root-locus of the system using the Matlab command of "rlocus" for the positive values of gain.(b) Using the root-locus you plotted, write the range of gain for stability of the system(c) What would be the value of the gainto have a closed-loop pole at -2.5?PD ControllerPlantFind it by hand and show it on theroot-locus you plotted.(d) Where would be the second pole forthe same value of gain?Find it by hand and show it on theR(s)C(s)G(s)Gp(s)root-locus you plotted.(e) Suppose that the plant has an additional unstable pole at +4 and hence looks as follows,s+ 3Gp(s) = s(s + 1)(s – 4)Plot the root-locus of this new system, Ge(s)G(s), for the positive values of gain in Matlab.() Using this root locus, write the stability range for gain of this new system.(g) What would be the frequency of sustained oscillation in Hz?(h) Plot this response for the first 4-5 periods and show that the response confims what you found in (g).

Problem 8. For the PD controlled positioning system, where Ge(s) = K(s+ 2) and Gp(s) =+1) (a) Plot the root-locus of the system using the Matlab command of "tlocus" for the positive values of gain. (b) Using the root-locus you plotted, write the range of gain for stability of the system (c) What would be the value of the gain to have a closed-loop pole at -2.5? Find it by hand and show it on the root-locus you plotted. (d) Where would be the second pole for the same value of gain? Find it by hand and show it on the PD Controller Plant R(s) C(s) G(s) Gp(8)

Problem 8. For the PD controlled positioning system, where Ge(s) = K(s+ 2) and Gp(s) =+1) (a) Plot the root-locus of the system using the Matlab command of "tlocus" for the positive values of gain. (b) Using the root-locus you plotted, write the range of gain for stability of the system (c) What would be the value of the gain to have a closed-loop pole at -2.5? Find it by hand and show it on the root-locus you plotted. (d) Where would be the second pole for the same value of gain? Find it by hand and show it on the PD Controller Plant R(s) C(s) G(s) Gp(8)

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...

See similar textbooks

Similar questions

If the roots of the characteristic equation are -3,0 then the system is _________________________. Marginally stable Conditionally stable Stable Unstable
A resistor (R = 1 Ω), inductor (L = 0.1 H) and capacitor (C = 0.1 F) are connected in series, and the current I(t) through the circuit is measured as shown in the image below Assuming that the capacitor is uncharged at t = 0, and that the circuit is electrically small (such that propagation times between components can be neglected), find (or approximate where necessary) for times t = [0 : 0.1 : 0.4] (i.e. do not calculate at t = 0.5) : (shown in the image below)
The structural engineering design section within the engineering department of a regional electrical utility corporation has developed several standard designs for a group of similar transmission line towers. The detailed design for each tower is based on one of the standard designs. A transmission line project involving 50 towers has been approved. The estimated number of engineering hours needed to accomplish the first detailed tower design is 126. Assuming a 95% learning curve, a. What is your estimate of the number of engineering hours needed to design the eighth tower and to design the last tower in the project? b. What is your estimate of the cumulative average hours required for the first five designs?
A system has the following characteristic equation: s + s + 3 + 2s + 2 = 0 Using the Routh-Hurwitz method, check
Consider the given circuit with vi=3V, R1=20K, Rf=50K, R2=10K, R3=20K, C=2μF. Assuming that the capacitor is an open circuit, determine vo.
The characteristic equation of a system is given as s3+25s2+10s+50=0. What is the number of the roots in the right half s-plane and the imaginary axis respectively?
Using the diagram capacitor circuit and values provided, find ZC1, Z T, i, VR1, and Vc1
Select the forward path gain (M ktop) for the system for the SFG diagram given below
Which row represent the most stable system and why? nyquist and root locus plot attached.
Compute the convolution y(n) = x(n) * h(n) , Where x(n) = {1,1,0,1,1} and h(n) = {1,-2,-3,4} , Using : Graphical Method
Find out following:i. Sketch the root locus.ii. The number of branches of the root locus.iii. The value of ? and gain ? where the locus crosses the ??-axis.iv. The breakaway and break-in point on the real axis.
Which of the following is not true? a.Increasing system gain increases stability b.poles farther to the left of imaginary axisimprove speed c.steady-state errors are important in the studyof unstable systems d.multiple poles on the imaginary axis improvessystem stability