Attracting Law Based Discrete-time Controller Designs: Methodology And Implementation

The design of discrete-time controller is an important research direction of industrial field. With the advantage of high dynamical response speed and position tracking precision,the servo systems have been used widely in the industrial control. With servo systems taken as background, this thesis gives precision control method, which is suitable for the controlled position and repeatable operation, in order to provide high performance control technology of servo systems. The main work is summarized as follows:1. An exponential attracting law based controller design method is proposed for discrete-time systems with input/output description. A measure of disturbance-rejection is embedded in the attracting law to form the ideal error dynamics, by which the discrete-time controller is derived. Theoretical analysis shows that there are the bounds for three layers in the system, such as the bounds of the monotonically decreasing region, absolute attractive layer, and steady-state error. The steps for tracking error to converge to the origin/steadystate error bound without/with the disturbances are found. The correctness of the bounds for three layers and convergence steps is demonstrated by a numerical simulation.2. The chattering can be eliminated through replacing the sign function with the saturation function or ek/(|ek| + δ), δ > 0 for the chattering problem of the exponential attracting law. To characterize the converging performance and steady-state performance, the monotonically decreasing region, the absolute attractive layer bound and the steady-state error band of the tracking error are derived theoretically. Numerical simulation is given to verify the correctness of the bounds for three layers and the effectiveness of the proposed method.3. With the introduction of dead-zone sign function and interval function, the finitetime-dead-zone attracting law is formed, and the developed controllers ensure the tracking error to approach to the origin. For characterizing the tracking performance and the convenience in adjusting the controller parameters, we derive the expressions for the range ofthe steady-state error and the boundary between the monotonically decreasing region and the absolute attractive layer. Both the correctness of the bounds for three layers and the effectiveness of the proposed method are illustrated by a numerical simulation.4. An adaptive switching gain based attracting law approach is proposed for discretetime systems with input/output description. This method can automatically tune switching gain according to vary speed of closed-loop system uncertainties, and directly presents properties of the error-dynamics. In order to characterize the tracking performance, we give the steps for tracking error to converge to the origin, and derive the expressions for the range of the steady-state error and the absolute attractive layer. Numerical simulation is given to verify the feasibility and effectiveness of the presented control method.5. An attracting law based design of discrete-time repetitive controller is presented for systems with periodic reference/disturbance signals. A measure of disturbance-rejection is embedded in the attracting law to form the ideal error dynamics, by which the discrete-time repetitive controller is derived. For characterizing the tracking performance and the convenience in adjusting the controller parameters, we derive the expressions for the range of the steady-state error, the boundary of the monotonically decreasing region and the absolute attractive layer, and the steps for tracking error to converge to the origin/steady-state error bound without/with the disturbances are found. The developed repetitive controller is not only effective for rejecting the periodic disturbances, but also ensures chattering avoidance.The effectiveness of the proposed method is demonstrated by a numerical simulation.6. The 1/M-period repetitive controller is proposed for periodic reference/disturbance signals and reducing the data memory requirements. Comparing with the full-period one,the memory needs of the 1/M-period controller are the 1/M of the full-period one. A unitvector-continuous attracting law is presented to form the ideal error dynamics, by which the 1/M-period repetitive controller is derived. The controller parameters can be set to fulfill the tracking performance requirements for the bounds for three layers such as the monotonically decreasing region, the absolute attractive layer, and the steady-state error.Both the correctness of the bounds for three layers and the effectiveness of the proposed1/M-period repetitive controller are illustrated by a numerical simulation.7. The PMSM control system experimental platform is constructed to demonstrate the validity of the discrete-time controllers. The mathematical model of the motor is obtained by applying the least square algorithms. Based on it, the discrete-time controllersare designed. Periodic tracking and position control are involved in this experiment. The experimental results of the servo systems show the effectiveness of the proposed control method.