Linear Stage PID Control

PID-based DC motor linear stage position control and trajectory tracking using MATLAB/Simulink.

A complete simulation of a DC-motor-driven linear stage implementing plant modeling, PID controller design, robustness testing, disturbance rejection, sensor noise, and real-time MATLAB visualization.

---

Table of Contents

• Overview
• System Architecture
• System Parameters
• Controller Design
• Key Results
• Visualization
• Project Structure
• Getting Started
• Experiments Covered
• Modeling Limitations

---

Overview

This project models and controls a DC-motor-driven linear stage using MATLAB/Simulink. The control goal is precise position tracking — demonstrated with a 50 mm target — under realistic conditions including actuator saturation, sensor noise, quantization, and external disturbances.

Tools: MATLAB R2026a · Simulink · Control System Toolbox

---

System Architecture

Reference → Error → PID Controller → Actuator Saturation (±10 V)
         ←  Sensor (noise + quantization)  ←  DC Motor + Lead Screw → Platform Position

Logged signals:

Signal	Description
out.r_out	Reference position
out.y_actual	True physical position
out.y_measured	Measured (noisy) position
out.u_pid	PID command (before saturation)
out.u_sat	Actuator command (after saturation)
out.tout	Simulation time

---

System Parameters

DC Motor

Parameter	Symbol	Value
Armature resistance	R	2 Ω
Armature inductance	L	0.2 H
Torque constant	Kt	0.05 N·m/A
Back-EMF constant	Ke	0.05 V·s/rad
Rotor inertia	J	1×10⁻⁵ kg·m²
Viscous friction	b	1×10⁻⁵ N·m·s/rad

Linear Stage

Parameter	Symbol	Value
Platform mass	m	1 kg
Stage damping	bx	2 N·s/m
Lead-screw pitch	p	0.005 m/rev

The pitch-to-radius conversion factor k = p / (2π) ≈ 7.958×10⁻⁴ m/rad maps motor angle to linear displacement.

---

Controller Design

The plant transfer function maps voltage to linear position. Four controllers were compared:

Controller	Kp	Ki	Kd
P	10–100	—	—
PI	100	2–20	—
PD	100	—	1
PID (final)	100	2	1

Final PID transfer function:

C(s) = 100 + 2/s + s

Actuator limits: ±10 V (assumed driver limit).

---

Key Results

50 mm Step Response (±10 V)

Metric	Value
Rise Time	1.335 s
Settling Time	3.214 s
Overshoot	1.37 %
Final Position Error	−0.634 mm
Sensor Difference	0.001 mm
Peak PID Command	9.945 V

50 mm Ramp Tracking (0.01 m/s, ±10 V)

Metric	Value
Max Tracking Error	6.074 mm
RMS Tracking Error	4.444 mm
Steady-state RMS Error	1.612 mm
Peak Actuator Command	0.739 V (no saturation)

---

Visualization

The final MATLAB visualization (animate_final_stage.m) renders a 4-panel real-time animation:

Panel	Content
Physical Stage	Motor, rail, lead screw, moving platform with position markers
Position Tracking	Reference vs true vs measured position
Tracking Error	Position error in mm over time
Controller Output	PID command and actuator command vs ±10 V limits

---

Project Structure

linear-stage-pid-control/
├── README.md
├── linear_stage_model.m              # Plant + PID setup, analysis, and simulation script
├── linear_stage_model_simulink.slx   # Simulink model (full closed-loop simulation)
├── animate_final_stage.m             # 4-panel real-time MATLAB visualization
├── figures/                          # Exported plots and screenshots
│   ├── simulink_model.png
│   ├── controller_comparison.png
│   ├── controller_commands.png
│   ├── step_50mm.png
│   ├── ramp_50mm.png
│   ├── visualization.png
│   └── visualization_demo.gif
└── slprj/                            # Simulink build artifacts (auto-generated)

---

Getting Started

Prerequisites

• MATLAB
• Simulink
• Control System Toolbox

Running the Model

1. Clone the repository

   git clone git@github.com:<your-username>/linear-stage-pid-control.git
   cd linear-stage-pid-control

2. Open MATLAB and set the working directory to the repo root.

Ramp Tracking Setup

Configure ramp parameters before simulation:

target_position = 0.05;    % 50 mm
ramp_slope      = 0.01;   % m/s  (reaches target in 5 s)
buffer_time   = 6;       % s

ramp_time     = target_position / ramp_slope;   
sim_stop_time = ramp_time + buffer_time;       

3. Run the setup and simulation script:

   run('linear_stage_model.m')

4. Launch the real-time visualization after simulation:

   run('animate_final_stage.m')

---

Experiments Covered

Experiment	Description
Plant Analysis	Poles, zeros, open-loop step response
Controller Comparison	P / PI / PD / PID with gain sweeps
Load Robustness	Jeq ×0.8 / ×1.0 / ×1.3
Friction Robustness	beq ×0.5 / ×1.0 / ×2.0
Actuator Saturation	±10 V nominal · ±0.5 V severe
Disturbance Rejection	Input disturbance, max deviation 0.095 mm
Sensor Noise	Gaussian noise, std 1.227 mm
Quantization	Quantization-only vs combined noise
Step Positioning	50 mm step, ±10 V
Ramp Tracking	50 mm ramp at 0.01 m/s, ±10 V
Real-time Visualization	4-panel animated MATLAB figure

---

Modeling Limitations

The model is a linear approximation. Effects not included:

• Coulomb / static friction
• Lead-screw backlash and efficiency
• Motor current limiting and thermal behavior
• Structural flexibility
• Exact torque-speed curve

Possible future extensions: anti-windup, feedforward, friction identification, hardware implementation.