Titre : Embedded Convex Optimization for Control of Synchronous Machines
Résumé : This work focuses on the practical implementation of advanced control strategies for permanent-magnet synchronous motors (PMSMs), specifically covering trajectory generation, control law synthesis, and embedded real-time computation. The work is motivated by the need to bring control theory closer to industrial practice, particularly in motor drive systems, by embedding complex algorithms directly into low-cost microcontrollers.
First, we focus on embedded control directly into the microcontroller, to allow fully autonomous and adaptive motor control without external intervention. This is achieved by designing a lightweight linear matrix inequality (LMI) solver that runs as a low priority task alongside the fast control loop. The solver can recompute or update the control law during operations, using minimal computational resources. This approach is particularly interesting for industrial applications, as it allows real-time adaptation to changing operating conditions or system uncertainties, without requiring off-line recalibration or expert tuning. Furthermore, it enables the deployment of advanced control strategies in cost-sensitive environments where computational power is limited. The experimental results confirm the feasibility and effectiveness of this integrated optimization framework.
Second, we explore speed and torque control law synthesis, with a focus on robust and performance-guaranteed control strategies. Two approaches are explored. The first is a robust H2 state-feedback controller for interior permanent-magnet synchronous motors (IPMSMs) with norm-bounded parametric uncertainties. This method uses convex optimization via LMI to ensure performance and stability while requiring only a few physically meaningful tuning parameters, making it accessible to practitioners. The second approach employs a linearization-free controller within a linear parameter-varying (LPV) framework. By formulating a constrained H2 problem with speed-dependent gains and avoiding exact feedback linearization, this method improves robustness to measurement noise and cross-coupling effects in IPMSMs. Both control strategies are experimentally validated and demonstrate improved performance over traditional controllers.
Third, we address optimal torque control (OTC) problem through constrained optimization for two types of machines: surface-mounted permanent-magnet synchronous motor (SPMSM) and IPMSM. For the SPMSM, the Karush-Kuhn-Tucker (KKT) approach provides an analytical solution for feedforward optimal current reference generation for SPMSM. The analytical solution ensures that the voltage, current, torque, and speed constraints are met. Building on this foundation, we consider the more complex OTC problem for the IPMSM. Due to its non-convex structure including a non-affine equality constraint, a closed-form analytical solution is not available. To address this, we reformulate the problem through a change of variable, leading to a convex formulation with a single decision variable. We introduce a formal approach using sum-of-squares (SoS) programming to prove the convexity of OTC formulation for a given motor. This step guarantees global optimality and enables the use of efficient real-time embedded solvers. Finally, we implement an interior point method to solve the convex OTC problem for the IPMSM in real time.
Across these contributions, a consistent effort is made to experimentally validate the proposed algorithms on available SPMSM and IPMSM test benches.
