# Predictive Speed-Control Algorithm Based on a Novel Extended-State Observer for PMSM Drives
## 1 Introduction  
Permanent-magnet synchronous motors (PMSMs) are extensively used in the field of electric vehicle (EV) drive systems, robots, and CNC machine tools, because of its advantages in compact structure, reliability, high efficiency, and power density. The traditional proportional integral (PI) controller with cascade control structure is most commonly used for speed control of PMSMs. PI control method is simple and reliable, and the controller can be turned without knowledge of the mathematical model. However, in above applications, excellent dynamic response and high-precision tracking performance are the most important requirements. Simultaneously, due to the existence of inevitable model uncertainties and external disturbances, the general linear control methods cannot satisfy the requirement in high-performance applications of PMSM control systems. To improve the performance of the control system, many advanced nonlinear control methods have been developed in recent years, such as linearization control [1], adaptive control [2, 3], sliding mode control [4, 5], fuzzy control [6], and neural network control [7, 8]. These control methods can improve the performance of the motor in different aspects. Recently, as a practical and advanced industrial control technology, model predictive control (MPC) has attracted wide attention. MPC requires the explicit use of a dynamic model to predict process outputs of the future, then the future control action is obtained according to optimization of a target function or a cost function at each sampling time [9]. The application of MPC in PMSM has been mentioned in [10, 11]. In [10], according to the linear discrete time model of PMSM, a predictive control method is used in the speed and current loop, and a disturbance model is embedded in the speed loop to improve the robustness of the motor. In [11], a novel predictive controller is proposed whichcombines the speed and current loop together, and through optimizing a cost function consisting of a future speed tracking and \(d-q\) axis current error, the future control action can be derived. They are all studies based on the discrete time model of system, and the control strategies based on online optimization suffer from a heavy computational burden. In addition to above predictive methods, a generalized predictive control method for nonlinear system based on the continue time model is reported [12; 13] and used in PMSM control systems [14; 15]. Because there is no need for online optimization, the amount of calculation is decreased. In [14], a nonlinear predictive controller for PMSM is designed, and the load torque as a disturbance variable is estimated by an observer. In [15], the predictive control is applied in the speed and current loop, respectively, then a disturbance observer is designed to estimate the parametric uncertainties and the load torque value. According to the above literature, the MPC method is applied to the controller design and enhances the control performance of PMSM drive systems. Although the mentioned predictive control methods above have many advantages in motor control, MPC is still a model-based control method, and it does not work for the parameter variations and external load disturbance. To achieve an accurate control of the motor, the disturbances should be accurately estimated and compensated. There are many observers for disturbances estimation, such as unknown input observer [16], disturbance observer [17; 18], extended-state observer [19; 20; 21]. The applications of the observer for PMSM drive systems are presented in [18; 19]. In [18], the sliding mode disturbance observer is used to restrain external disturbance which can improve the anti-disturbance capability of the PMSM drive systems. In [19], an extended-state observer is applied to the speed controller of PMSM to estimate disturbance.