Objectives

• To develop MATLAB Simulink models for continuous and digital PI control systems.
  
• To simulate and compare the performance of continuous and discrete (digital) PI controllers for different sampling periods: $T_s=0.5$, $1.0$, and $2.0$ seconds.
  
• To analyze the effect of sampling period on control performance and stability.

Problem Statement

In practical control systems, continuous-time controllers are often implemented digitally using sampling and zero-order hold (ZOH) techniques. The sampling period significantly affects control accuracy and stability — too slow a sampling rate degrades performance, while too fast a rate increases computational cost.

The process under consideration is represented by the following transfer function:

$$\begin{array}{}\text{(1)}& G_p(s)=\frac{5e^{-2s}}{(7s+1)(s+1)}\end{array}$$

An output disturbance enters through the following transfer function:

$$\begin{array}{}\text{(2)}& G_d(s)=\frac{1.4e^{-3s}}{(10s+1)}\end{array}$$

You are required to implement and compare continuous and digital PI control systems for this process using MATLAB Simulink. The digital controller should use a zero-order hold and sampler, and the sampling period should be varied as described in the objectives.

Methodology

1. Simulink Model Development
   • Create a combined Simulink model that includes:
     • The process $G_p(s)$
       
     • The disturbance path $G_d(s)$
       
     • A continuous PI controller
       
     • A discrete PI controller implemented with Zero-Order Hold (ZOH) and Sampler blocks
       
   • Configure the sampling period $T_s$ for the digital controller as 0.5, 1.0, and 2.0 seconds.
     
   • Use the same controller gains for both implementations.
2. PI Controller Tuning
   • Tune a continuous PI controller for the process using Control System Designer or IMC-based tuning.
     
   • Record the controller gains ($K_c$, ${\tau }_I$).
     
   • Verify the closed-loop response for reference tracking and disturbance rejection.
3. Digital PI Controller Conversion
   • Discretize the continuous PI controller using the Tustin (bilinear) or backward Euler method.
     
   • Implement the digital controller in Simulink using either:
     • The Discrete PID Controller block, or
       
     • The continuous PID block with sample time = $T_s$.
       
   • Ensure a zero-order hold (ZOH) is used between the digital controller and the process.
4. Simulation Setup
   • Simulate step changes in the setpoint and output disturbance for both the continuous and digital control loops.
     
   • Run simulations for $T_s=0.5$, $1.0$, and $2.0$ seconds.
     
   • Observe and record key performance parameters: rise time, overshoot, settling time, and steady-state error.
5. Performance Comparison
   • Compare continuous and digital control performance using time-domain plots.
     
   • Analyze the degradation in response with increasing sampling time.
     
   • Discuss the trade-off between sampling speed, control accuracy, and computational cost.

Report Format

Your report (maximum 5 pages excluding submission details) should include:

0. Submission Details: Include a brief table at the beginning of the report with the following information:

Lab Title:	Lab 08 – Digital Control	Student Name	ID
Unit:	CHEN4011	Student 1	12345678
Date:	12 October 2025	Student 2	87654321

1. Objective & Problem Statement

   Summarize the aim of digital control implementation and explain why sampling period selection is important. Include the process and disturbance transfer functions.

2. Methodology & Implementation

   Describe the structure of the Simulink model and key components (ZOH, sampler, discrete PID). Explain how the PI controller was tuned and discretized. Provide screenshots of the Simulink model and show where the sampling period is defined.

3. Results

   Present time-domain responses (setpoint tracking and disturbance rejection) for both continuous and digital controllers. Show results for $T_s=0.5$, $1.0$, and $2.0$. Include a table summarizing rise time, settling time, overshoot, and steady-state error for each case.

4. Analysis and Discussion

   Compare performance between continuous and discrete systems. Discuss how the sampling period influences controller accuracy and stability. Explain any performance degradation at larger $T_s$. Relate findings to real-world digital control implementation.

5. Conclusion

   Summarize key findings. Recommend an appropriate sampling period based on the trade-off between speed and accuracy. Reflect on the importance of sampling rate selection in digital control system design.

Assessment Rubric (20 Marks Total)

No	Section	Marks	Evaluation basis
1.	Objectives & Problem	2	Clarity of objectives; explanation of digital control context
2.	Methodology and Implementation	5	Correct Simulink setup; explanation of ZOH/sampler; controller tuning process
3.	Results	5	Quality and labeling of response plots; completeness of tabulated performance data
4.	Analysis and Discussion	6	Comparison across sampling periods; insights on performance degradation
5.	Conclusion and Presentation	2	Summary of findings; clarity, formatting, and presentation quality