Objectives

1. To design a cascade control system using nested feedback loops with primary (outer) and secondary (inner) controllers.

2. To implement and compare cascade vs. conventional (single-loop) control strategies for setpoint tracking and disturbance rejection.

3. To develop a MATLAB Simulink model for the cascade control system and tune both controllers using the PID Tuner or analytical methods.

Process information

Case 1

The transfer functions for the primary process and secondary (inner-loop) process are:

$$\begin{array}{}\text{(1)}& \begin{array}{rl}\text{ Primary Process: }{G}_p(s)& =\frac{2.5\exp (-4s)}{(5s+1)}\\ \\ \text{ Secondary Process: }{G}_s(s)& =\frac{-1.6\exp (-1.2s)}{1.5s+1}\end{array}\end{array}$$

Case 2

$$\begin{array}{}\text{(2)}& \begin{array}{rl}\text{ Primary Process: }{G}_p(s)& =\frac{0.2\exp (-5s)}{s}\\ \\ \text{ Secondary Process: }{G}_s(s)& =\frac{2\exp (-0.8s)}{2s+1}\end{array}\end{array}$$

Methodology

For each case in Section 2

1. Tune a PI controller using a classical PID tuning formula.

2. Develop the Simulink models for the feedback control using primary loop only and cascade control strategy (with a tightly tuned inner loop).

3. Evaluate the control performance for:

   • Setpoint tracking (Step input in setpoint)

   • Disturbance rejections for input disturbance.

   • Disturbance rejections for output disturbance.

Error Metrics

Use the following metrics to quantify performance:

1. Integral of Time-weighted Absolute Error (ITAE): $$ITAE={\int }_0^{T}t\cdot |e(t)|dt$$

   ITAE penalizes large errors that persist for a long time.

2. Integral of Absolute Error (IAE): $$IAE={\int }_0^T|e(t)|dt$$

   IAE gives a measure of the total absolute error over time and is sensitive to both the magnitude and duration of the error.

3. Integral of Squared Error (ISE): $$ISE={\int }_0^{T}e(t{)}^{2}dt$$

   ISE penalizes larger errors more heavily than smaller errors, making it useful when minimizing large errors is particularly important.

4. Integral of Time-weighted Squared Error (ITSE): $$ITSE={\int }_0^{T}t\cdot e(t{)}^{2}dt$$

   ITSE is similar to ISE but includes a time-weighting factor, penalizing errors that persist for longer periods.

5. Peak Absolute Error (PAE):

   PAE is the maximum absolute error that occurs over the time period of interest. It’s a measure of the largest deviation from the desired output.

6. Settling Time:

   The settling time is the time required for the error to fall within a specified percentage (e.g., 2% or 5%) of the final steady-state value and stay within that range.

7. Rise Time:

   The rise time is the time required for the system response to rise from a specified lower percentage to a specified higher percentage of its final steady-state value.

8. Overshoot:

   Overshoot is the percentage by which the system’s response exceeds its final steady-state value. It gives an indication of the stability and damping of the system.

Report Format

Your report (5 pages maximum) should include the following:

0. Submission Details

   Include a brief table at the beginning of the report with the following information:

   Lab Title:	Lab 02 - Cascade control	Student Name	ID
   Unit:	CHEN4011	Student 1	12345678
   Date:	12 August 2025	Student 2	87654321

1. Objective & Problem Statement

   Briefly describe the goal of using cascade control and summarize the given process dynamics.

2. Methodology & Implementation

   • Describe the setup of feedback-only and cascade control models
   • Provide Simulink diagrams with brief explanations
   • Explain controller tuning methods used for inner and outer loops

3. Results

   • Show the system response for both control strategies under:

     • Setpoint tracking
     • Input and output disturbance rejection

   • Include well-labeled plots with appropriate axes, legends, and annotations.

   • Summarize relevant performance metrics such as IAE, ITAE, overshoot, rise time, and settling time for each scenario.

4. Analysis and Discussion

   • Compare and interpret the performance of the two control strategies: feedback-only vs. cascade control.

   • Address the following points:

     • Does cascade control improve disturbance rejection compared to feedback-only? Why?
     • Does cascade control provide better setpoint tracking? Explain using plots and metrics.
     • How robust is each control configuration under ±10% model mismatch in time constants or gain?
     • Quantitatively assess and compare the performance of each method using the selected metrics (e.g., IAE, overshoot, settling time).

5. Conclusion

   • Summarize your key observations
   • State when cascade control is most advantageous

Assessment Rubric (20 Marks Total)

No	Section	Marks	Evaluation basis
1.	Objectives & Problem	2	Clarity of problem definition; articulation of objectives
2.	Methodology and Implementation	4	Correctness and clarity of Simulink models; explanation of PID tuning strategy
3.	Results	4	Quality, relevance, and labeling of plots; completeness of performance data
4.	Analysis and Discussion	6	Insightful interpretation; robustness; comparisons of control strategies
5.	Conclusion and Presentation	4	Coherent summary; quality of writing, formatting, and visual presentation