Analog Control System

MATLAB simulation of a closed-loop analog control system with transport delays, sensor dynamics, and actuator saturation.

Plant Model

The controlled plant consists of:

• Integrating element — 1 / (s·Tᵢ)
• First-order inertia — Kₚ / (1 + s·Tₚ)
• Second-order oscillatory element — 1 / (1 + s·a₁ + s²·a₂)
• Transport delay — e^(−s·T₀)

The full open-loop plant transfer function:

                    Kₚ · e^(−s·T₀)
G(s) = ——————————————————————————————————————————
        s·Tᵢ · (1 + s·Tₚ) · (1 + s·a₁ + s²·a₂)

Controller Design Methods

Folder / File	Method
szukanie_Kp.m	Proportional gain sweep (overshoot & settling time)
LEAD/	Lead compensator via root-locus
LAG/	Lag compensator (Bode design)
LEAD-LAG/	Combined Lead-Lag compensator
STATE FEEDBACK/	Full state-feedback with Luenberger observer
tuning_z_n.m	Ziegler-Nichols PID tuning
pid_optim.m + pid_cost.m	PID optimization (ITAE criterion, fminsearch)
main.m	Unified simulation — compares selected controller vs. baseline

Simulation Details

• Time-domain simulation using trapezoidal (Heun) integration
• Actuator saturation at ±5 V
• Step and ramp reference inputs
• Comparison plots of designed controller vs. proportional baseline

Requirements

• MATLAB R2020a or later
• Control System Toolbox

Quick Start

% Run the main simulation (default: Lead-Lag + State Feedback comparison)
main

% Sweep proportional gain to find optimal Kp
szukanie_Kp

% Optimize PID parameters
pid_optim