State control of a DC motor
Designing and comparing PI, lead and nested-loop controllers for a DC motor, against tight stability and response targets.
- Year
- 2015
- Context
- Control engineering, Loughborough University
- Tools
- MATLAB, Simulink, Control theory
The aim
Model a DC motor and design a controller that tracks a demanded speed and position quickly, accurately and stably.
The plant
The motor was modelled from its physical constants: torque and back-EMF constants of 0.03, armature resistance of 2.7 Ω and rotor inertia of 4.73 × 10⁻⁵ kg m². The model was built and simulated in MATLAB and Simulink.
The design targets
- Gain margin of at least 6 dB and phase margin of 60°.
- Rise time of about 0.31 seconds.
- Zero steady-state error.
- Overshoot under 20%.
Approach
Three designs were developed and compared against those targets: a proportional-integral (PI) controller, a lead compensator, and a nested-loop design with an inner speed loop and an outer position loop. Each was tuned against the stability margins and checked in simulation.