CN4227R Advanced Process Control

Project 2 Due on 2 April 2014

Consider a 22 process transfer function given by

++

++=

1210

1122

174

1210

)( 7.4

5.3

se

se

se

se

sG ss

ss

(a) For the diagonal pairing, a 22 decentralized controller can be designed by the

independent design (ID) procedure, where the first PI controller is designed while

the second control loop is put on the manual mode. Specifically, this PI controller is

designed entirely based on the (1,1)-th element of G(s). Likewise, PI controller for the

second loop is designed based on the (2,2)-th element of G(s). The following ITAE

tuning relations are used to tune the two PI controllers.

916.0)(586.0 =KKc ;

165.003.1 =I

where K, and denote the process gain, time constant, and time-delay of a process

model, respectively, while Kc and I are the PI parameters.

Implement the decentralized PI controller designed above using the Simulink to

obtain process output response, i.e. y1 vs. time and y2 vs, time, for the respective unit

step changes in the set-points of y1 and y2 at 5=t . The entire simulation time is 80

unit time.

(b) Repeat part (a) to design a 22 decentralized controller when the off-diagonal

pairing is considered and obtain servo response for the same set-point changes

described in part (a).

(c) By comparing the servo performance in parts (a) and (b), briefly discuss the effect

of pairing on the control performance from the perspective of RGA analysis or/and NI

criterion, if applicable.

(d) For the undesirable pairing discussed in part (c), re-design a new 22

decentralized controller for better servo response of the entire 22 decentralized

control system, for example improvement from originally unstable response to stable

response, reduction of large overshoot in the originally highly oscillatory response,

etc.

Remarks

For consistencys sake, PI controller implemented in your Simulink file for this Project should use the ideal PID block, which has been uploaded in the

IVLE.

The PID equation in ideal PID block is formulated as P + I/s + D*s. Therefore, P = Kc, I = Kc/I and D = Kc*D, where Kc, I, and D are the

parameters of PID controllers defined in the textbook.

Lastly, for consistencys sake again, parameters in Configuration Parameters under Simulation menu bar given at the top of Simulink files are specified

as: Type = fixed-step, Solver = ode4 (Runge-Kutta), and Fixed-step size =

0.05.