Combined Control Of DC Motor And Piezoeletric Ceramic For Position Tracking

The permanent magnet DC motor has the advantages of good starting performance,large overload capacity,easy control,and smooth and stepless speed regulation in a short time.Therefore,permanent magnet DC motors are widely used in large precision machine tools for relay protection.No matter in the medical field,industrial field,or IC integrated manufacturing,DC motors are used in positioning platforms due to their sufficient travel and low cost.However,in the case of high requirements for precision tracking technology,the DC motor cannot reach the desired accuracy.In order to overcome this shortcoming,we have adopted a method of using piezoelectric ceramics in conjunction with a permanent magnet DC motor.Piezoelectric ceramics are widely used because of the advantages of low power consumption,large driving force,high positioning accuracy,and fast response speed.These advantages are complementary to DC motors.Piezoelectric ceramics are often used to achieve high-precision positioning with small strokes.However,the non-hysteresis characteristic of piezoelectric ceramics is an important factor that causes system instability and will affect control accuracy.So how to compensate for hysteresis nonlinearity and then make up for this shortcoming is an important subject of research.This paper intends to combine DC motors and piezoelectric ceramics to realize the upper-level planning and lower-level composite control,and then to achieve precise tracking positioning control.1.Model establishmentFirstly,the mathematical model of DC motor is established according to the torque mechanism and circuit mechanism of the motor,and the positioning system model of permanent magnet DC motor with the ball screw mechanism is established by combining with the ball screw mechanism to convert the rotating motion of the motor into linear motion.Then,the nonlinear characteristics of piezoelectric ceramics are analyzed,and the Hammerstein model is established for the hysteresis nonlinear characteristics.The nonlinear part of the model was represented by the Bouc-Wen model,and the parameters are identified by particle swarm optimization(PSO).Thelinear part of the Bouc-Wen model is equivalent to a second-order system.In order to eliminate the influence of the hysteresis nonlinearity of the piezoelectric ceramics,the inverse of the Bouc-Wen model is obtained to compensate the hysteresis characteristics,and then a piezoelectric ceramic model with the hysteresis nonlinearity compensated is obtained.2.Design of upper-level model predictive controllerFirst,a permanent magnet DC motor and piezoelectric ceramic parallel system is established based on the basic characteristics of the parallel system model.A model predictive controller based on the state space expression is designed.Each component value in the weight matrix is adjusted to make the sum of displacement of DC motor and piezoelectric ceramics in parallel reach the expected displacement curve together.And achieve the desired displacement curve together,and then obtain the state quantities that the DC motor and the piezoelectric ceramic need to reach,that is,the control objectives of the lower-level DC motor and the piezoelectric ceramic.3.Design of lower-level sliding mode controller and backstepping controllerAccording to the calculation results of the upper-level MPC controller,the two state quantities obtained are used to design the sliding-mode controller of the lower-level motor and the piezoelectric ceramic backstepping controller that shields the hysteresis nonlinearity,so that the two can reach lower-level control objective calculated by MPC.And then the simulation analysis is performed.4.Design of triple-step controller for nonlinear DC motorThe modeling in Chapter 2 ignores various frictional forces of DC motors,but frictional forces are difficult to ignore in motion control theory.In order to improve the control accuracy of the lower-level control,we consider to control the motor system containing frictional forces.From the traditional PID control algorithm to the nonlinear triple-step control method,the principles and design methods of class-like steady-state control,reference feedforward control,and error feedback control are described respectively.The error feedback uses the form of PID controller.A triple-step nonlinear control method is designed to realize the lower-level control of the DC motor.The obtained results are simulated to prove the rationality of the proposed scheme and the designed controller is robust.