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 T1 = 4 min. and T2 = 6 min. respectively. The steady state gain is 5 and dead time is 12 min. The loop is to be controlled to achieve a desired dynamics of first order with time constant Td = 2 min. and zero steady-state offset. Produce solutions to the following questions.
(i) Identify the plant transfer function and the desired closed-loop system 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.
(ii) Design a feedback control system with a PID controller designed using the closed-loop Ziegler-Nichols empirical method. The Simulink model used in the experiment to obtain the sustained output curve should be displayed. The sustained output curve should also be displayed. The controller design must be presented.
(iii) Design a Smith Predictor control system for the given plant with the controller designed using the Direct Synthesis Method. A block diagram must be shown to demonstrate the control system structure. The design details are also required.
(iv) Simulate the three control systems designed using the three methods with a unity step input for 100 minutes. The simulation must use one Simulink model with three sub-models, each for a control system. Display the Simulink model and sub-models, and present the simulation parameter setting. Display the three outputs and the set-point in one figure for comparison. Display also the three corresponding control variables in another figure. Compare the three output curves and comment on the performances of the three control systems.
(v) Write a report with content, a brief introduction, description of the process to be controlled, presentation of the control system design with each method, simulation model and sub-models, control systems outputs and corresponding control variables, and finally the comparison, comments and conclusion.