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In this article, a predictive position control method based on a novel input-constrained nonlinear dynamic model (NDM) is proposed for time-varying position tracking of planar motors. The motivation lies in the possible utility of this method for motion systems. This method uses NDM subject to input constraint to deal with actuator saturation rather than uses a constrained optimization problem, such that it differs from conventional model predictive control. The NDM is represented in state–space equations (SSEs) to describe dynamic behaviors of the system constituted by the planar motor and an input saturation module. In contrast to linear SSEs, this model has the same linear vector-matrix form; the difference is that it applies saturation functions of states to replace states of state equation in linear SSEs for representing nonlinearity. By employing a self-designed neural network, the parameters of this model are determined via experimental sample data. With this model, a nonlinear multistep predictive model subject to input constraint is developed. Additionally, an explicitly analytical state feedback control law is approximately deduced by solving an unconstrained optimization problem subject to the nonlinear predictive model. Finally, simulation and experimental results show the effectiveness of the proposed method.

This article proposes a predictive position control of long-stroke planar motors to achieve micrometer-scale positioning under long-stroke time-varying trajectory tracking for use in high-precision positioning applications. The motivation consists in the potential application of model predictive control in long-stroke planar motors for high-precision positioning systems. This control is the first of its kind for planar motors. A dynamic model of a long-stroke planar motor developed in the laboratory is built, and then a predictive model is established to predict future positions of the motor. An additional term is introduced to a cost function to improve the positioning accuracy, which provides an output feedback control action to the motor for reducing the model error of the predictive model. By minimizing the cost function, an analytically explicit solution of the optimal control sequence is obtained, which makes the computational burden of the controller low. The stability of the control system is discussed based on the closed-loop state-space model. Moreover, the selection of stable control parameters is theoretically given. Simulation and experimental results demonstrate the effectiveness of the proposed control method of long-stroke planar motors for use in high-precision positioning applications.

This article proposes a predictive position control method of planar motors using trajectory gradient soft constraint with attenuation coefficients in the weighting matrix to achieve high-precision, time-varying, and long-stroke positioning. Based on a built dynamics model of a planar motor developed in the laboratory, a predictive model is established to predict the future positions of the motor. To improve the positioning precision, a soft constraint defined by a trajectory gradient difference between the gradients of the reference position and predictive position sequences is introduced to the cost function. Then, an explicitly analytical solution of the optimal control is obtained by minimizing the cost function. To highlight the stronger effects of the trajectory gradients closer to the current time, the attenuation coefficients are applied to the weighting matrix of the added soft constraint. The stability of the control system is proved employing the linear quadratic optimal control method and the Lyapunov stability theory. Moreover, the time complexity is discussed based on the analytical control action to show low computational burden of the proposed method. Finally, the given simulation and experimental results demonstrate the effectiveness of the proposed method to achieve high-precision time-varying positioning for planar motors.

An accurate mover position is important for a planar switched reluctance motor (PSRM) to achieve precision positioning; however, position sensors are susceptible to the influence from harsh conditions and are relatively expensive. In this article, an assistant-mover-based position estimation method is proposed to increase the reliability and reduce the cost of a PSRM system. The method is based on a mapping relationship between the flux density and position of the assistant mover. First, the configuration of the assistant movers is presented. Then, an analytical model of the flux density of the assistant mover is developed by using an equivalent magnetic circuit method. Based on the analytical model, the parameters of the assistant mover are determined. According to the flux density characteristics, a position estimation algorithm with the advantages of not requiring previous experimental data, simple computation, and small memory consumption is developed. Moreover, considering the deviation in the characteristics of each assistant mover, a compensation strategy is proposed to obtain better position estimation accuracy. Finally, the proposed method is implemented with the PSRM system. The effectiveness of the proposed position estimation method is verified experimentally.

This paper proposes a novel maximum-force-per-ampere strategy for the current distribution of planar switched reluctance motors (PSRMs) for efficiency improvement. This strategy is the first of its kind for planar motors, and it is used to generate the desired thrust force with the minimum sum of squares of the three-phase current. To formulate this strategy, a constrained optimization problem with time-varying parameters is first developed. Then, the problem is transformed into an unconstrained problem with a barrier function. Additionally, a self-designed adaptive genetic algorithm is introduced to solve the unconstrained optimization problem for locating the optimal currents. Comparative studies of the proposed and conventional strategies for a PSRM system are carried out via simulation and experiment, and planar trajectory tracking for the system with the proposed strategy is experimentally performed. The validity of the proposed strategy is also verified.