摘要：针对直流电机伺服系统三闭环PID控制问题，采用LQR方法整定相应的PID参数。根据理论建模与实验建模相结合的方法，建立直流伺服系统的数学模型；在此基础上给出三闭环PID控制系统的结构，并转换成能够利用LQR方法整定相关参数的等效结构。针对电机伺服系统的位置控制，引入位置偏差以及位置偏差的积分作为新的状态变量，并结合电机系统的转速、电流以及位置构成新的状态空间方程，针对新的状态空间模型采用LQR计算反馈矩阵，进而根据对应关系求出三闭环PID控制系统各控制器的参数。最后，进行了仿真实验以及物理实验，实验结果验证了该方法的有效性。
关键词：PID控制器；LQR；三闭环控制；直流电机；伺服控制

Abstract: Aim at three closed loop PID control DC motor servo system,the LQR theory was adopted to set PID parameter.According to the combination of theoretical modeling and experimental modeling, the mathematical model of DC servo system was present.The structure of three closed loop PID control system was given, and then it was translated into the equivalent structure which could use LQR setting parameter.For motor position control of the servo system, the position deviation and the integration of position deviation were as new state variables, and then connecting with the motor position, motor speed and current of the system. The new state space equation was present.According to a new state space model, the LQR theory was adopted to calculate the feedback matrix, and then according to the corresponding relations between the three closed loop PID control system and LQR feedback matrix, the PID parameter was obtained.Finally, the simulation and physical experiment was present, the experimental results verified the effectiveness of the proposed method.
Key words: PID controller；LQR；three closedLoop Control；DC motor；servo system