Nonlinear Model Predictive Control of a Magnetic Levitation System Using Artificial Protozoa Optimizer

A magnetic levitation system (Maglev) is a sensitive, multi-parameter, nonlinear, and unstable system that is utilized to levitate a ferromagnetic object in free space. Due to its vast applications, various research studies in the field of control strategy have become extremely important and challenging. This work proposes the design of a nonlinear model predictive (NMPC) control scheme for the object position control against the nonlinearities and uncertainties of a Maglev system. A novel bio-inspired Artificial Protozoa Optimization (APO) algorithm is used to fine-tune the NMPC parameters, which include best weighting matrices ( ), shorter prediction horizons ( ), and shorter time steps ( ) to minimize the objective cost function. The effective performance of the NMPC is verified using simulation-based results in MATLAB. The CasADi toolbox is utilized to solve nonlinear optimization problems and handle the nonlinearity of the Maglev system model. Simulations are implemented for three trajectories tracking (step, sine, and square) with 20% and without Maglev parameters perturbations. To prove the superiority of the proposed controller, comparisons are made with the conventional Linear Quadratic Regulator (LQR) and proportional-integral-derivative (PID) controllers. Two performance indices are introduced, Integral of Squared Error (ISE) and Integral of Absolute Error (IAE), to examine the tracking performances of the NMPC, LQR, and PID controller. The NMPC controller has shown more efficient performance and accurate results than other controllers. The contributions of this work include a new optimization technique of APO, a new engineering application of the APO integrated with NMPC to control a Maglev system, consideration of inherent nonlinearities and system constraints, and robustness improvement under perturbation.