This project presents the modelling, simulation, and control of a 3-DOF Cartesian robot manipulator using MATLAB/Simulink.
The system is first derived using Lagrangian dynamics, then implemented in Simulink to simulate its behaviour, and finally controlled using decentralized PID controllers to achieve accurate trajectory tracking.
This project reflects a complete robotics workflow from dynamic modelling to control system implementation.
The manipulator consists of three prismatic joints operating along:
- X-axis (linear motion)
- Y-axis (sinusoidal motion)
- Z-axis (step motion)
The system dynamics are derived using a Lagrangian formulation to obtain the equations of motion for each joint.
The dynamic behaviour of the Cartesian manipulator is derived using a Lagrangian formulation, capturing the relationship between applied forces and joint motion.
- Kinetic energy is based on translational motion of each link
- Potential energy is influenced by gravity along the Z-axis
- Euler–Lagrange equations are used to derive the system dynamics
This results in second-order differential equations describing each joint:
- X-axis: q̈x = Fx / mx
- Y-axis: q̈y = Fy / my
- Z-axis: q̈z = (Fz − mg) / mz
These equations form the foundation of the simulation model and are used to compute acceleration, velocity, and position over time.
A decentralized PID control architecture is used:
- Each joint is treated as an independent system
- Control input is computed using tracking error
- Feedback loop ensures stability and accuracy
The controller minimizes the error between:
- Desired trajectory
- Actual joint position
The control system is implemented in Simulink using a decentralized PID structure.
Each prismatic joint (X, Y, Z) includes:
- Reference trajectory input
- Error calculation (desired − actual)
- PID controller
- Dynamic system (acceleration → velocity → position)
- Feedback loop
The following diagram shows a zoomed-in view of the control loop for a single prismatic joint.
- PID controllers successfully reduce tracking error
- System stabilizes quickly after initial transients
- Minor overshoot observed in step response
- Controller remains stable under parameter variation
- Demonstrates strong robustness and reliability
The full system, including both dynamic modelling and control implementation, is developed in Simulink.
The model file is available in the models/ folder.
- MATLAB
- Simulink
- Adaptive or robust control methods
- Model predictive control (MPC)
- Multi-axis coupling effects
- Real-world hardware implementation
Jessica Sutherns https://github.com/jessysutherns
This project demonstrates a complete robotics pipeline including:
- Dynamic modelling of manipulators
- Simulation of physical systems
- Control system design
- Performance evaluation
It highlights how modelling and control work together to enable precise and stable robotic motion in real-world applications.