The Improved Fractional Order PID Control Algorithm And Its Application

Fractional calculus is a generalization of integer calculus.With the improvement of fractional calculus theory,the applications of fractional calculus theory in control field haves gradually become a research hotspot.Fractional order PID controller is an important achievement in the application of fractional order calculus theory.It has five control parameters,so it is difficult to tune the control parameters.At present,fractional order PID controller has been widely used,but for some complex systems,fractional order PID controller is still difficult to achieve satisfactory control results.In view of the above problems,this paper mainly does the following research works:The optimization process of fractional order PID control parameters based on traditional quantum particle swarm optimization algorithm is easy to fall into local optimal solution.In this paper,an improved quantum particle swarm optimization(IQPSO)algorithm is proposed by adding particle update and particle diffusion to the optimization process.The simulation results show that the IQPSO algorithm is advanced in parameter optimization.The fractional order PID controller approximated by low-order integer transfer function is easy to implement,but its accuracy is low.In this paper,an improved low-order approximation method of fractional calculus operator is proposed by using IQPSO algorithm,which effectively improves the low-order approximation accuracy of fractional calculus operator.The effectiveness of this method is verified by simulation.In order to improve the control performance of fractional order PI controller in permanent magnet synchronous motor control,a fractional order PI controller with integral limit is proposed based on the analysis of the function of fractional order PI controller.To further improve the control performance of fractional order PI controller with integral limit,a fractional order PI controller with integral limit tracking is proposed by using discrete load torque observer to limit the output of fractional order integrator.The simulation results show that the fractional order PI controller with integral limit tracking has better control performance.Experiments on speed control of permanent magnet synchronous motor(PMSM)are carried out to verify the effectiveness of the algorithm.An improved discrete scheme of time-domain approximation method is proposed to solve the problem that fractional order PID controller with memory length can easily lead to oscillation of controlled system.The improved discrete scheme of time-domain approximation method is compared with two Z-domain approximation methods.The results show that the improved discrete scheme has better control performance.On the basis of the improved discrete format,the fractional order PID controller with optimal single-step control parameters and the fractional order PI controller with variable order are proposed.The control performances of the two controllers are simulated and analyzed.The two controllers are applied to the output voltage control of SEPIC circuit and the speed control of PMSM respectively.The experimental results verify the effectiveness of the two controllers.