Coursework Specification and Marking Scheme

A concentration control loop in an industrial chemical process can be represented by a second order dynamics with a long transmission delay. The two time constants of the second order dynamics are $T_1=4$min and $T_2=6$min respectively. The steady state gain is $5$ and the dead time is $12$min. The loop is to be controlled to achieve a desired dynamics of first order with time constant $T_d=2$min and zero steadystate offset for a step reference. Produce solutions to the following questions.

$2$

$($i$)$ Identify the plant transfer function. Then, design a feedback control system with the controller designed using Direct Synthesis method, where the time$-$delay is approximated using the first$-$order Taylor expansion. Implement the controller with a standard industrial PID controller.

Simulate the designed control system for $100$ minutes using a unity step input as the reference signal. Display the output and the set$-$point in the top figure, and the corresponding control variable $u(t)$ in the bottom figure.

$[20$ marks$]$

$($ii$)$ Design a feedback PID control system for the given plant, where the PID controller is designed using the closed$-$loop Ziegler$-$Nichols empirical method. The Simulink model used in the experiment to obtain the sustained oscillatory output curve should be displayed, and the output curve should also be displayed. The controller design procedure should be presented. Do the same simulation and display the results as in $($i$).$

$[20$ marks$]$

$($iii$)$ Design a Smith Predictor control system for the given plant with the controller designed using the Direct Synthesis method. A block diagram should be shown to demonstrate the control system structure. The design details are also required. The designed controller should be implemented using a PID controller. Do the same simulation as in $($i$).$

$[20$ marks$]$

$($iv$)$ Construct a Simulink model with three sub$-$models with each for a control system designed in the above. Run the simulation and display the results with three outputs and the set$-$point in the top figure, and the three control signals in the bottom figure. Compare the performance of the designed three control systems and comment on the performance.

$[20$ marks$]$

$($v$)$ Write a formal report to present the design, simulations and the results. The report should have a content list, a brief introduction, description of the process to be controlled, presentation of the control system design using each method, simulation models, control systems outputs and corresponding control variables, and finally the comparison, comments and conclusion.

The report should be written logically$,$ clearly and completely. Mathematical expressions would be presented using Microsoft Equation. All figures would have title, labels, units for variables and legends as appropriate.