📐 Digital Control Laboratory

Course: Digital Control Systems — Electrical Engineering
Environment: MATLAB / Simulink
Topics: Z-transform, discrete-time design, frequency response, PID/lead-lag controllers

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🗂️ Lab Overview

Lab	Topic	Files
Lab 2	Z-Transform & Discrete-Time Basics	Lab2/lab2_ztransform.m
Lab 3	Frequency Response & Bode Analysis	Lab3/lab3_bode.m
Lab 4	PID Controller Design	Lab4/lab4_pid.m
Lab 5	Lead-Lag Compensator Design	Lab5/lab5_lead_lag.m
Lab 6	Closed-Loop Sensitivity & Robustness	Lab6/lab6_sensitivity.m

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🔬 Lab 2 — Z-Transform & Discrete-Time Analysis

Objective: Analyse discrete-time signals using Z-transform, compare with continuous-time equivalents.

Key operations performed:

• Forward/inverse Z-transform via iztrans and manual partial fractions
• Pole-zero mapping (pzmap) to verify stability
• Step response comparison: continuous vs. sampled system

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🔬 Lab 3 — Frequency Response & Bode Analysis

Objective: Design a discrete controller satisfying gain/phase margin specs using Bode plots.

Key operations performed:

• Open-loop Bode plot (bode) with margin analysis (margin)
• Lead compensator placement to meet φₘ ≥ 45°
• Closed-loop verification: step, bode(feedback(...))

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🔬 Lab 4 — PID Controller Design

Objective: Design a discrete PID controller and analyse step response performance.

Parameter	Value
Rise Time	< 0.5 s
Overshoot	< 10 %
Settling Time	< 2 s

Key operations performed:

• Ziegler-Nichols tuning in discrete domain
• Anti-windup implementation
• Root-locus analysis (rlocus) to verify pole placement

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🔬 Lab 5 — Lead-Lag Compensator Design

Objective: Design a cascaded lead-lag compensator to improve transient and steady-state response.

Key operations performed:

• Phase-lead design for bandwidth improvement
• Phase-lag design for steady-state error reduction
• Combined lead-lag: series(C_lead, C_lag)
• Sensitivity / complementary-sensitivity plot

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🔬 Lab 6 — Closed-Loop Sensitivity & Robustness

Objective: Analyse sensitivity functions and verify robustness margins.

Key operations performed:

• Mixed sensitivity design: minimise ‖Wp·S‖∞
• Bode plot of S (sensitivity) and T (complementary sensitivity)
• lsim with step + sinusoidal disturbance to validate rejection

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🛠️ How to Run

% In MATLAB, navigate to the lab folder and run:
run('Lab2/lab2_ztransform.m')
run('Lab3/lab3_bode.m')
% ... etc.

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📎 Notes

• All scripts require MATLAB R2021a or later with the Control System Toolbox
• Simulink models (.slx) are included where applicable
• Results match those submitted in the formal lab reports