Stuck on this problem, an explanation of the answer would be very much appreciated!!
Stuck on this problem, an explanation of the answer would be very much appreciated!!
Problem 4. The open-loop transfer function of a unity feedback system is 20 G(s) S+1.5) (s +3.5) (s +15) (a) Design a lag-lead compensator for G(s) using root locus so that the closed-loop system satisfies the design specifications. (b) Design a PID compensator for G(s) using root locus so that the closed-loop system satisfies the design specifications. Design specifications -SSE to a unit step reference input is less than 0.02. Overshoot is less than 20%. Peak time is less than...
Problem 4. The open-loop transfer function of a unity feedback system is: 20 (s+1.5)(s 3.5) (s 15) G(s) (a) Design a lag-lead compensator for G(s) using root locus so that the closed-loop system satisfies the design specifications (b) Design a PID compensator for G (s) using root locus so that the clos ed-loop system satisfies the design specifications. Design specifications .SSE to a unit step reference input is less than 0.02. Overshoot is less than 20% Peak time is less...
Consider the sontrol system shown in the figure below: R(S) + E(s) C(s) K (s + 4)(s + 6) g) Sketch the uncompensated system root locus showing all details. (5 Points) h) Find the dominant closed loop poles of the uncompensated system to operate with a 16.3% overshoot and peak time tp = 0.7255 (make sure to show this point on the Root Locus) (5 Points) (s+z) Now we want to design a PI compensator of the form to increase...
A plant with the transfer function Gp(s)-- with unity feedback has the root locus shown in the figure below: (s+2)(s+4) Root Locus 1.5 C(s) 0.5 0.5 1.5 .3 Real Axis (seconds) (a) Determine K of Gp(s) if it is desired that the uncompensated system has a 10% OS (overshoot) to a step input. (4 points) a 5% overshoot and a peak time Tp 3.1 meets the requirements described in part (b) and achieves zero steady state (b) Compute the desired...
4. A lead compensator with a transfer function Ge(s)=K(+0.5/(s+3) has been designed for a Space vehicle with the transfer function 1/s' such that at the dominant closed loop poles are located at -1 +/-j1. (0) What is the angle deficiency of the uncompensated system at the designed point provided by the location of the dominant poles? Show that the compensator provides the necessary lead angle at the designed point to satisfy the root locus angle criterion. What value of K...
4) 3s points 11. Given the unity feedback system of Figure P9.1 with G(s) K (s + 6) do the following: [Section: 9.3 a. Sketch the root locus. b) Using the operating point of -3.2+j2.38 find the gain K. c) if the system is to be cascade-compensated so that T, -1 sec, find the compensator compensator zero is at -45. pole if the d) Sketch the root locus for the new compensated system. 4) 3s points 11. Given the unity...
1. Using the MATLAB rltool command (or rlocus and rlocfind), plot the K > 0 root locus for What is the value of the largest damping ra- 2+2s+1 s(s120)7,7 -2,12). 1 + KL(s) = 0, where L(s) = tio associated with the pair of complex poles? At which value of K is it achieved? Turn in a printout of your plot showing the location of the poles on the damping ratio line that you found. 2. Suppose the unity feedback...
Please solve parts (a) and (b) neatly and show problem solving. Ignore reference to part 1, but please still plot the root loci. For the system given in Figure 1 a) Design a PD compensator with the transfer function: to give a dominant root of the closed-loop characteristic equation of the compen- sated system at s -1+j1 (i.e., a settling time Ts of less than 6 seconds and a maximum overshoot Mo of less than 10%). Required Pre-Practical work] (b)...
4. A lead compensator with a transfer function Ge(s) = K(s+0.5)/(s+3) has been designed for a Space vehicle with the transfer function 1/s? such that at the dominant closed loop poles are located at -1 +/-jl. (1) What is the angle deficiency of the uncompensated system at the designed point provided by the location of the dominant poles? Show that the compensator provides the necessary lead angle at the designed point to satisfy the root locus angle criterion. (iii) What...
Question 1 (60 points) Consider the following block diagram where G(s)- Controller R(s) G(s) (a) Sketch the root locus assuming a proportional controller is used. [25 points] (b) Design specifications require a closed-loop pole at (-3+j1). Design a lead compensator to make sure the root locus goes through this point. For the design, pick the pole of the compensator at-23 and analytically find its zero. (Hint: Lead compensator transfer function will be Ge (s)$+23 First plot the poles and zeros...