环形单级倒立摆系统的改进PSO-PID控制研究

Improved PSO-PID Control of Single Rotary Inverted Pendulum System

为实现环形单级倒立摆的稳定性控制,设计了一种改进的基于粒子群算法的积分分离PID控制算法.首先通过拉格朗日方程推导出环形单级倒立摆系统的数学模型,然后用matlab计算发现系统不稳定,因此需要设计外部控制器加以调节.本文提出了改进粒子群算法(PSO)来整定PID控制器参数,在此基础上设计了一种改进的积分分离的PID控制器,在比例和积分项前加入连续变化的函数作为系数以防止积分饱和.最后在matlab中分别用基PSO-PID控制和基于改进积分分离的PSO-PID控制对环形单级倒立摆进行仿真.仿真结果表明,在改进积分分离的PSO-PID控制下,系统中连杆和摆杆的超调量均下降至0,调节时间分别缩短至0.8s和0.9s.这说明本文设计的控制方法能有效使环形单级倒立摆在较短的时间内达到稳定.

In order to realize the stability control of the single-stage inverted pendulum, an improved integral separation PID control algorithm based on particle swarm optimization is designed. First, the mathematical model of the single-stage inverted pendulum system is deduced by the Lagrangian equation, and then the system is unstable by matlab, so it is necessary to design the external controller to adjust it. Then, an improved particle swarm optimization algorithm（PSO） is proposed to set the parameters of the PID controller. On this basis, an improved integral-separated PID controller is designed to add the continuously changing function as a coefficient before the ratio and integral to prevent integral saturation. Finally, in the matlab, the PSO-PID control and the PSO-PID control based on the improved integral separation are used to simulate the single-stage inverted pendulum. Under the control of PSO-PID with improved integral separation, the overshoot of connecting rod and pendulum in the system decreased to 0, and the adjustment time is shortened to 0.8s and 0.9s respectively. The control method designed in this paper could effectively stabilize the single-stage inverted pendulum in a short time.