Aiming at the problem that controller parameters are not easy to be selected in industrial process control, a method for calculating controller parameters based on fractional order transfer function is proposed. A fractional order transfer function is set as the objective, and the form and parameters of fractional order controller are obtained by calculation.
This method has the characteristics of simple calculation and easy selection of parameters. The method is validated by first-order and second-order unstable systems.
The simulation results show that the method has good practical maneuverability and the fractional-order controller has good robustness. In industrial process control, the accuracy of controller parameters determines the stability of the whole industrial process, so the selection of controller parameters becomes the most important part of industrial process control. An expert PID parameter selection method [1] has been proposed and successfully applied in the main temperature control system, but the parameter tuning of this method is complex.
In references [2] and [3], thermostatic element the parameters of cascade controller are successfully obtained and used in hydraulic simulator and CVT speed ratio control system, but the algorithm is very complex and difficult to operate.
Firstly, an objective transfer function is set up, and the form and parameters of the controller are obtained by calculation. Then, the controller is put into the system to control the system. This method is simple and easy to operate. The obtained controller has good control and robustness, and has good practical application. The common definition of fractional calculus is proposed by Riemann-Liouvile, Grunwald-Letnikov and Caputo.
Among them, sum is real number, sum is upper and lower limit of integral, and it is Euler gamma function. In physical systems and practical engineering, the definitions of Gunwald-Letnikov and Riemann-Liouvile are equal, commonly known as Letnikov-Liouvile (LRL). Although LRL’s initial value problem can be solved mathematically successfully, it becomes meaningless to give an appropriate physical explanation for the initial value problem. Among them: sum is the upper and lower limit of integral. But when the initial values are zero, the definitions of Caputo and LRL are the same. Among them, sum is a constant and sum is an order (both integer and decimal).
The selected objective transfer function should converge. The adjustment time of the selected target transfer function should be appropriate.
Select transfer functions with fewer links as far as possible.
The peak value of step response of the selected transfer function is appropriate. The specific form is determined by the form of sum. It can be seen from the transfer function that the poles of the system are in the right half plane and belong to the unstable system.
The solid line is the step response curve of the original controlled object, and the dotted line is the step response curve of the system when the system gain is changed to 4. It can be seen that the controller has strong robustness at this time. In order to solve the problem of controller parameter selection in industrial process control, fractional order model is used as the objective function of the system, and a fractional order controller is obtained. The application of fractional order controller in the original model can achieve good control effect. The robustness of the controller is tested, and the robustness is still very good even if the system gain is changed a lot. The simulation results show that this method has practical application.