Optimal Predefined-Time Tracking Control for Multimotor Driving Servo Systems With Unknown States

This paper investigates the optimal predefined-time tracking control and observation problem for multimotor driving servo systems with unknown states. First, a novel predefined-time stable criterion is introduced as the theoretical foundation, which enables a smaller convergence domain. Building on this criterion and leveraging the duality between the optimal observer and linear quadratic tracking (LQT) control, an optimal predefined-time observer is proposed to estimate the unknown system states. This framework avoids the computational complexity usually involved in solving the Algebraic Riccati Equation (ARE) and conducting online optimization using approximate dynamic programming (ADP). Then, we develop an optimal predefined-time controller comprising a load tracking controller and a multimotor synchronization controller. The optimal predefined-time load tracking controller is designed by employing a new nonlinear command filter with an error function, addressing the control singularity problem. Additionally, the proposed approach minimizes certain performance measure while ensuring that both the tracking error and state observation error converge to zero within a predefined time. Finally, the control and observation performances are validated on a four-motor servo system platform. Note to Practitioners - Due to the increasing demand for advanced system drive capabilities in industrial production, using multiple motors to simultaneously drive heavy loads has become an effective solution to overcome the limitations of single-motor drive capacity. This paper addresses the optimal predefined-time tracking control and state estimation problems for multimotor drive servo systems with unknown states, which have broad practical applications, such as artillery system control and radar servo system control. In predefined-time control, optimizing the performance of both the controller and the observer is crucial for enhancing control precision. However, this issue has been rarely considered in the existing literature. To tackle these issues, this paper proposes an optimal predefined-time controller and observer for multimotor drive systems based on a predefined-time stability criterion. This approach not only guarantees that the error converges within a predefined time but also simultaneously optimizes the performance of both the controller and the observer. Furthermore, to address the singularity issue in the backstepping method, this paper introduces a predefined-time nonlinear command filter. Compared to existing methods, the proposed observer and controller reduce computational complexity and overcome the limitations of systems with relative degree one, thereby improving the method's applicability.