Deep learning based model predictive controller on a magnetic levitation ball system

Abstract

The magnetic levitation (maglev) ball system is a prototypical Single-Input-Single-Output (SISO) system, characterized by its pronounced nonlinearity, rapid response, and open-loop instability. It serves as the basis for many industrial devices. For describing the dynamics of the maglev ball system precisely in the pseudo linear model, the long short-term memory (LSTM) based auto-regressive model with exogenous input variables (LSTM-ARX) is proposed. Firstly, the LSTM network is modified by incorporating the auto-regressive structure with respect to sequence input, allowing it to deduce a locally linearized model without the need for Taylor expansion. Then, the LSTM-ARX model is transformed into a linear parameter varying (LPV) state space model, and upon this foundation, a model predictive controller (MPC) is proposed. Specifically, when deducing the MPC, the deep learning-based model is linearized by fixing its state input at the current state, so that the nonlinear, non-convex optimization problem can be converted to a finite-horizon quadratic programming problem, thereby deriving the explicit form of MPC. To further enhance the efficiency of the controller in real-time control tasks, a predictive functional controller (PFC) is proposed. It employs multiple nonlinear functions to fit the control sequence, thereby reducing the number of decision variables of the on-line optimization problem in MPC. The proposed controller was successfully applied to the real-time control of the maglev ball system. Simulation and real-time control experiments have validated the improvement in transient performance and efficiency of the LSTM-ARX model-based PFC (LSTM-ARX-PFC).

Keywords: LSTM-ARX; MPC; Magnetic levitation system; Nonlinear model; PFC.