Design And Application Of A Class Of Adaptive PD/PI Controller

Any actual engineering system has some degree of uncertainty.On the one hand,the designers may not be able to obtain the structure and parameters of the mathematical model of the controlled object accurately;On the other hand,the external environment is always difficult to predict even if it can be equivalently replaced by disturbing links.Facing all kinds of uncertainties,how to design a control function with good performance is the focus of adaptive control research.As a control strategy in modern control which is widely used,the problem of parameter tuning in PID controller design has not yet formed a perfect theoretical system,thus causing its engineering application to be limited to a large extent.Therefore,combining adaptive control with classical PID control,on this basis,the parameter tuning method of the controller is discussed,which undoubtedly has profound theoretical research and practical application significance.In this paper,the adaptive PD and PI control strategies based on robust adaptive theory are proposed to solve the existing defects in PID controller parameter tuning.The parameters of the designed controllers can be adjusted independently and automatically in real time according to the tracking error of the controlled second-order system.The main work of this paper is summarized as follows:First of all,two kinds of research objects are given.Based on the force analysis of single particle model combined with Newtonundefineds second law,the basic dynamic equation is given.On this basis,two kinds of cases are considered:first,the second partial derivative of the main part to the state variable of the system is equal to the non-zero constant,and one of the special cases is selected,and the first kind of research object of this paper is obtained.Secondly,the second partial derivative of the main part to the state variable of the system is equal to 0,and the general expression in this case is obtained directly,that is,the second kind of research object of this paper.Secondly,the adaptive PD/PI controller is designed for the above two kinds of research objects.In this paper,the appropriate and innovative filter variables are selected,and a reasonable scaling inequality is constructed,finally,the adaptive law of the controller coefficient and the online updating law of the parameters are obtained.Once the disturbance factor is produced,the adaptive tracking control algorithm can detect the uncertain signal in time and automatically adjust the controller gain immediately,so as to eliminate the tracking error.Finally,a complete proof of the stability of the adaptive control algorithm is given based on the stability theory of the Liapnov direct method.In addition,the Matlab simulation experiments are carried out by selecting the engineering background which meet the conditions,and the simulation results also prove the effectiveness of the algorithm.