I)
Ii) .& Iii)
Gain Margin and phase Margin we got from bodeplot .
Bode plots are used to gain insight on the frequency response of a transfer function. The magnitude plot (generally displayed in dB) is used to understand the gain of the system and the phase plot is used for phase change from input to output
A Bode Plot is a useful tool that shows the gain and phase response of a given LTI system for different frequencies. Bode Plots are generally used with the Fourier Transform of a given system. An example of a Bodemagnitude and phase plot set.
Root locus plot is used to understand how the poles of a system vary based on system parameters (e.g., controller gain, model parameters, etc.)
Root locus starts from open loop pole(K=0) to open loop zero(K=INFINITY).
The main and the foremost advantage of root locus is to check the system behaviour by adjusting the value of gain K . The adjustment in the value of K will trace the roots accordingly on the R-H plane and will give the conditions for the system to be overdamped, underdamped, crictically damped, overdamped or undampedaccording the the respective value of k. If:-
ROOTS ARE SAME AND REAL - CRITICALLY DAMPED SYSTEM
ROOTS ARE REAL AND DISTINCT- OVERDAMPED
ROOTS ARE PURELY IMAGINARY- MARGINAL STABLE SYSTEM
ROOTS ARE COMPLEX CONJUGATE PAIRS- UNDERDAMPED
Also it gives the limit of K for which it can be varied until the system becomes unstable
Question 4 a) A simplified form of the open loop transfer function of a chemical process...
Question 4 a) A simplified form of the open loop transfer function of a chemical process as shown in Figure 4 is 1 G(S) = S(S + 3)(S2 + 25 + 2) where H(S) = 1. i. ii. Construct the root locus. (5 marks) From the root locus in (a), show the range of gain K at the root loci so that the system will stable. Discuss your answer. (2 marks) b) State two important parameters that you got from...
Question 4 a) A simplified form of the open loop transfer function of a chemical process as shown in Figure 4 is 1 G(s) = s(s + 3)(s2 + 2s + 2) where H(s) = 1. Construct the root locus. (5 marks) ii. From the root locus in (a), show the range of gain K at the root loci so that the system will stable. Discuss your answer. (2 marks) i. b) State two important parameters that you got from...
a) A simplified form of the open loop transfer function of a chemical process as shown in Figure 4 is 1 G(s) s(s + 3)(s2 + 2s + 2) where H(s) = 1. i. ii. Construct the root locus. (5 marks) From the root locus in (a), show the range of gain K at the root loci so that the system will stable. Discuss your answer. (2 marks) b) State two important parameters that you got from Bode plot method...
Question 4 a) A simplified form of the open loop transfer function of a chemical process as shown in Figure 4 is 1 GO) = 2(8 + 3)(8 +20 +2) where H(s) = 1 i. Construct the root locus. (5 marks) . From the root locus in (a), show the range of gain K at the root loci so that the system will stable. Discuss your answer. (2 marks) b) State two important parameters that you got from Bode plot...
G(s) Question 4 a) A simplified form of the open loop transfer function of a chemical process as shown in Figure 4 is 1 s(s+3)(s2 + 2s + 2) where H(s) = 1. i. Construct the root locus. (5 marks) ii. From the root locus in (a), show the range of gain K at the root loci so that the system will stable. Discuss your answer. (2 marks) b) State two important parameters that you got from Bode plot method...
A simplified form of the open loop transfer function of a chemical process as shown in Figure 4 is ?(?) = 1/ ?(? + 3)(?2 + 2? + 2) where ?(?) = 1. i. Construct the root locus. (5 marks) ii. From the root locus in (a), show the range of gain ? at the root loci so that the system will stable. Discuss your answer.
Control System 3) Consider the simplified form of the transfer function for position servomechanism used in an antenna tracking system as shown in Figure Q3. By using root locus technique: Error Els) C(s) R(s)+ s2 +4S +5 2.56S +12.8 Figure Q3 (a) Sketch its root locus (11 marks) (b) Find the value of K so that the damping ratio 0.342, and give all closed loop poles for the value of K. (9 marks) 3) Consider the simplified form of the...
[7] Sketch the root locus for the unity feedback system whose open loop transfer function is K G(s) Draw the root locus of the system with the gain Kas a variable. s(s+4) (s2+4s+20) Determine asymptotes, centroid, breakaway point, angle of departure, and the gain at which root locus crosses ja-axis. A control system with type-0 process and a PID controller is shown below. Design the [8 parameters of the PID controller so that the following specifications are satisfied. =100 a)...
Q1. Show analytically that the Root Locus for the unity feedback system with open loop transfer function: (a) [10 marks] K(s 4) (s + 2) is a circle, and find the centre and the radius. Determine the minimum value of the damping ratio and the corresponding value of K (b) The root locus of the open loop transfer function: [10 marks] s(s26s +15) is depicted in Figure Q1(b). Find the minimum value of gain K that will render the system...
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...