Multi-constrained Linear Systems With Pid Parameter Stability Region

To its good control effect,PID control technology has always been the dominant technology of actual industrial process control.Considering to that the system always need to meets some key performance of actual industrial process control,therefore,if we can get the stable region of PID controller parameters which meets various performances,we can design the PID controller conveniently.Based on the algorithm to determine the stable region of PID controller parameters of linear system without any performance,the paper gives an algorithm to determine the stable region of PID controller parameters of linear system which meets constraint of amplitude and phase margin.Firstly,based on Generalization of Hermite-Biehler theorem applying to complex polynomial, using the inverse Nyquist curve to determine the stable region of proportional gain.The stable region of intergral and differential gain corresponding to the given value of proportional gain is determined by using anti-clockwise rule and method to obtain the intersection of polygon.Thus,the stable region of PID controller parameters of linear system is determined.The paper also gives an algorithm to determine the stable region of PID controller parameters of linear system which meets constraint of settling time and overshoot.Corresponding to each value of propotional gain in the stable region that determined by system without any performance,the stable region of integral and differential gain which meets constraint of settling time and overshoot is determined in the stable region of integral and differential gain of system without any performance.Remove the propotional gain if there is no stable region of integral and diffenental gain with it.Then a smaller stable region of proportional gain is given.Thus,the stable region of PID controller parameters of linear system is detemined.Combining the two algorithms together,the paper gives several, main steps to determine the stable region of PID controller parameters of system which not only meets constraint of amplitude and phase margin but also meets constraint of settling time and overshoot.Finally,the paper design a interface based on MATLAB GUI,it can quickly,directly and accurately show the stable region of PID controller parameters of linear system which meets various performances.