Frequency analysis for K=1.
The calculation and plot has been done using MATLAB software.
Plots for gain K=12. Shown below
gain margin and phase margin is calculated below:
USE EXCEL i dont get what you mean!!! An industrial plant has the following transfer function:...
A unity feedback control system has the open loop TF as: \(G(s)=\frac{K(s+a+1)(s+b)}{s(s+a)(s+a+2)}\)a) Find analytical expressions for the magnitude and phase response for \(\mathrm{G}(\mathrm{s}) .\left[K=K_{1}\right]\)b) Make a plot of the log-magnitude and the phase, using log-frequency in rad/s as the ordinate. \(\left[K=K_{1}\right]\)c) Sketch the Bode asymptotic magnitude and asymptotic phase plots. \(\left[K=K_{1}\right]\)d) Compare the results from \((a),(b)\), and \((c) .\left[K=K_{1}\right]\)e) Using the Nyquist criterion, find out if system is stable. Show your steps. \(\left[K=K_{1}\right]\)f) Using the Nyquist criterion, find the range...
b- Consider a unity feed- back control system has (S+1 +)(S+2) (S+1-j) 3 4S2 6S + 4 a-Prove that as K-8 the gain margin-7.96 db at 2.45 rad/sec. and the phase margin 44.1 degrees at 1.56 rad/sec.? b-Sketch the polar plot? c-Sketch the Bode plot? d- Sketch the Nichols plot and Show Gm and Ym on the plots? e-Write short MATLAB program to solve a, b, c and d?
1. A unity feedback system has open-loop transfer function given by an 100 G(s)s2)(s +4) a. Use analytical techniques (i.e. without using any plots) to estimate the closed-loop: i. Resonant frequency, w (8 marks) ii. Resonance peak, Mp (in decibels) (2 marks) i. Phase at w = 3rad/s (2 marks) b. Obtain a table for the response of the open-loop transfer function for a set S of frequency values, where S {1.5,3,5,7, 10, 15, 20} rad/s (8 marks) Hence draw...
I got A,B,C done can you do D,E,F Also can you check my solutions please. Thank you ? Question 1 - Consider an unit feedback system whose open-loop transfer function is G(s)-k/ ((s + 1)(s 2 +4s 25)) A. Draw Bode plot of the open-loop system for k-75 B. Calculate the phase and magnitude of G(s) at 1 rad/s for k 75 C. Determine the cross-over frequency, and the phase and gain margins for k-75 (14 marks D. What is...
1. A unity feedback system has open-loop transfer function given by an 100 G(s)s2)(s +4) a. Use analytical techniques (i.e. without using any plots) to estimate the closed-loop: i. Resonant frequency, w (8 marks) ii. Resonance peak, Mp (in decibels) (2 marks) i. Phase at w = 3rad/s (2 marks) b. Obtain a table for the response of the open-loop transfer function for a set S of frequency values, where S {1.5,3,5,7, 10, 15, 20} rad/s (8 marks) Hence draw...
A unity feedback system has the following open-loop gain function 10 s(s+2) Use MATLAB to plot the Bode plot of this system Find the gain and phase margin. Identify these margins on the Bode plot. Is the G(s) a. b. system stable?
b) The Nyquist plot of a unity feedback control system is as shown in Figure Q5(b). Nyqulst Diagram x 10 1.5 1- System: N Real: -9.08e-005 0.5- Imag: -5.62e-006 Frequency (rad/sec): -104 -0.5 -15 -1.5 0.5 0.5 1.5 1 2.5 3.5 Real Axis x 10 Figure Q5(b) K If the transfer function of the system is given as G(s) (s+10)(s+50)(s+150) determine the following: The closed loop stability of the system using Nyquist Stability Criterion. i) ii) Gain margin and phase...
Let G,()+3s+5) , K-1 and Ge 1 I Determine the loop transfer function L(s)-KG.G. Use 'margin' command in matlab to generate the Bode Plot for L(s). (a) What are its gain and phase margins (these should be available in the plots). (b) Convert the gain margin in dB to absolute value. (c) For what value of the gain K would the closed loop system become marginally stable? (d) Show that, for this value of K, the closed loop system does...
A unity gain negative feedback system has an open-loop transfer function given by 4. s) = s(1 + 10s)(1 + 10s)? Draw a Bode diagram for this system and determine the loop gain K required for a phase margin of 20 deg. What is the gain margin? 5. We are given the closed-loop transfer function 10(s + 1) T(s) = 82+98+10 for a "unity feedback" system and asked to find the open-loop transfer function, generate a log-magnitude-phase plot for both...
The Bode diagram of the forward-path transfer function of a unity- feedback control system is obtained experimentally when the forward gain is fixed to certain value K. a) Find the gain and phase margin of the system from the diagram the best you can read. Is the system stable or unstable? Justify your answer. (25 points) b) Find out how much the gain must be changed from its original value for having a marginally stable system (25 points) Print and...