Linear Model Predictive Control Implementations on a Twin Rotor MIMO System

This thesis presents the design and implementation of a linear model predictive control (MPC) law on a Twin Rotor Multi-Input Multi-Output (MIMO) System (TRMS), a highly nonlinear aerodynamic system with very challenging cross-coupling dynamics. The TRMS has behaviours resembling those of a helicopter but with reduced complexity and requiring input constraints for a safe operation. MPC is used due to its suitability in handling multivariable systems and its unique ability to satisfy constraints as part of its optimisation process. Fast and high level linear MPC solvers were generated using CVXGEN, an online convex quadratic program (QP) optimiser, and implemented on the MATLAB Simulink platform. Through a comparison between the Linear Time-Invariant (LTI) MPC law used in this mthesis and an equivalent Linear Quadratic Regulator (LQR) solution, based on input amplitude and rate constraints imposed while tracking a constant command, simulation and experimental results show that MPC has a more economical control action and better state response. The MPC law is extended to the standard Linear Time-Varying (LTV) case (LT V1) where a new model is linearised at every sampling instant based on the current outputs and remains constant for all predictions in that sampling instant. A new LTV approach (LT V2) is presented in which new models are linearised at each sampling instant based on the current output as well as the outputs from the previous predictions except the first, and used for each state prediction in the optimal control problem at the next sampling instant. An ultra-fast MATLAB executable C++ function is developed which ensured the successful simulation and experimental validation of the LTV cases, making the model linearisation over 10 times faster in comparison with a standard MATLAB function. All MPC cases (LT I; LT V1; LT V2) were compared for command tracking and torque disturbance rejection. A push-pull solenoid is used for torque impulse disturbance which significantly reduces experimental error and ensures accurate repeatability. LT V2 showed better tracking and disturbance rejection while using less control effort, due to it being more sensitive to system dynamics while in operation, in comparison with LT I and LT V1. Offset-free control is achieved using a standard integral action (IA) approach, and compared with an output-feedback MPC disturbance model offset-free strategy in the literature. The easier to implement IA approach showed more satisfactory simulation and experimental results and is easily extended with better tracking results for LTV cases, a drawback of the disturbance model strategy. However, the IA approach is exposed to integrator windup and would therefore need an anti-windup strategy for systems at risk of input saturation. Constraints are successfully imposed on the cross-coupling dynamics of the controlled variables (pitch and yaw), proven through the avoidance of physical obstacles placed on the output’s path. This can be extended to the problem of obstacle avoidance by uncrewed aerial vehicles (UAVs).