Time Optimal Control of Second-Order Power Electronic Systems based on Pontryagin’s 5k Minimum Principle

Second-order power electronic systems are integral to many grid-tied and motor-drive applications, yet their inherent LC-filter dynamics often trigger undesirable oscillations and overshoot during transient events. These control challenges are further compounded by dc-link constraints, under which controller saturation degrades performance. Model predictive control (MPC) is commonly employed to handle such constraints, but its real-time implementation presents a fundamental trade-off: short prediction horizons lead to sub-optimal tracking, while long horizons deliver near-optimal performance at the cost of a prohibitive computational burden. As a result, previous approaches have been unable to achieve near-optimal reference tracking within the computational limits of standard microcontroller units (MCUs). To overcome these limitations, this paper proposes a time optimal control (TOC) scheme based on Pontryagin's minimum principle (PMP), tailored specifically for second-order systems in transient conditions. A rigorous mathematical derivation of the control scheme is presented, covering both undamped and damped systems across low- and high-frequency time-varying reference tracking scenarios. The resulting quartic equation is solved in a form that ensures real-time implementation. Experimental results show that the proposed TOC algorithms reduce total arithmetic operations by at least an order of magnitude compared to MPC, while maintaining excellent transient response and tracking accuracy.