System Stability in the Frequency Domain and in the s-Domain Bode Plots, Routh-Hurwitz Criterion of Stability
Consider a hydraulic control system under PID Control, represented by a diagram in Figure Q5.1.
The process transfer function is described as follows:
PID Controller series configuration
4 Gs= s+2s+2
R(s)
Y(s)
G(s)
1+1/g5
The PID controller transfer function has an Integral, and a Derivative Time Constant, as follows: T=0.06sec and a=0.1sec
Process
Figure Q5.1 - Closed Loop System with PID Control
Consider a hydraulic control system under PID Control, with time constants T and T as specified. Your task is to investigate the stability of the closed loop system by finding the range(s) of safe operating gains for the Proportional Controller Kp-
17 marks Write up the Open Loop transfer function for the system, and use Matlab to generate the Open Loop Bode Plots. Next, read off the plot the frequency (or frequencies)ose, and the corresponding value (or values) of Kcrit and place them in Table 5.1. Use Matlab to create a Root Locus plot for the system (rlocus function). Based on the shape of the Root Locus and on the readouts from Bode Plots, determine the safe range of the Proportional Gains for a stable operation of the closed loop system and place it in Table 5.1. Do not submit any plots.
213 marks Verify your findings by applying the Routh-Hurwitz Criterion of Stability. You should be getting the same results as in item 2. Show all the calculations, as no points will be given just for the final answers.
Table 5.1
Item 1 - Critical Gains:
Frequencies:
Safe Operating Range(s) based on shape of Root Locus:
Item 2 - Critical Gains:
Frequencies:
Safe Operating Range(s) based on Routh Array: