Top-Down" Controller Design by Pole Placement, Response Specifications, Second Order Model.
P Controller
Process
R(s)
K_{p}
Y(s)
A/(s(s + a))
Consider a unit feedback closed loop control system, as shown on the left. The Controller is in a configuration referred to as Proportional + Rate Feedback. Process parameters are:
Rate Feedback
(tau_{d}*s + 1)
A = 25 a = 5
The compensated closed loop step response of this system is to have the following specifications:
PO = 0% e ss( step (\%) =0\%, T settle(plus/minus 2%) =1 sec.
1) (5 marks) Substitute numerical values for the process, and derive the closed loop system transfer function in terms of Controller parameters, K_{\mathcal{D}} and tau_{d} . Write out the "as is" Characteristic Equation of the system. Next, find the closed loop transfer function for the uncompensated system, G clu (s) i.e. when K_{p} = 1 and tau_{d} = 0
2) (5 marks) Choose the appropriate locations for the Closed Loop system poles so that the specified requirements are met. Write out the "desired" Characteristic Equation of the system.
3) (5 marks) Complete the controller design so that all specs are met. Once you have the solutions for K_{p} and tau_{d} , write up the expression for the closed loop transfer function of the compensated system G clc (s) Place your results in Table 3.1.
4) (5 marks) Obtain the following transient performance specs: Percent Overshoot (PO), Settling Time (T settle(plus/minus 2%) ) and Steady State Error (e ss(step) \% ), for both closed loop transfer functions, the uncompensated G clu (s) and the compensated G clc (s) and place them in Table 3.2. Does your design meet the requirements? If not, what can be done to improve your design