Adaptive PID Control For Second Order Nonlinear Systems

PID controller is composed of three control structures: Proportion,Integral and Differential.Since the PID controller was proposed in the 1920 s and 1930 s,thanks to its simple structure,easy implementation,and good control effect,it has been rapidly developed and applied in the next few decades.In the current industrial control system,more than 90% of the industries use PID controllers,such as metallurgy,machinery,chemical industry,etc.However,in the actual industrial process control,many controlled objects have complicated process mechanisms,model non-linearity,time-varying parameters and uncertainties,and pure system lag,etc..due to load disturbances,noise and other factors,the model parameters and even the structure may change during the movement.In the above practical situation,it is necessary to set the PID parameters to be able to adjust online in real time,and not to rely excessively on the accurate mathematical model of the controlled system.This thesis designs the adaptive PID and PI algorithms that can realize real-time online adjustment for second-order nonlinear systems,and each algorithm parameter can be adjusted separately.The main work of this thesis is summarized as follows:(1)The APID(adaptive PID)and API(adaptive PI)tracking control algorithms applicable to second order nonlinear systems are developed.The proposed APID and API algorithms can automatically tune its gains to compensate system uncertainties.Rigorous stability proof for second order nonlinear systems with APID and API controller in the loop is provided.The most important point of these two control algorithms is to achieve the stability of the system,because an unstable system is unable to perform the intended task.At the same time,it is different from the very hot neural network PID or fuzzy PID that has been developed in recent years.Although some articles of neural network PID or fuzzy PID have also achieved good control results,they have not given strict stability proof.The algorithms in this thesis not only provides a strict proof of stability in theory,but it can also be clearly seen through simulation that these algorithms can indeed achieve good target tracking.(2)The three parameters P(proportional),I(integral),and D(differential)in the algorithm can be adjusted independently.They are all adjusted according to feedback state error.In the PID-like algorithm,the adjustment of the three parameters P,I,and D is connected through a common intermediate variable,three parameters will affect each other,and independent adjustment cannot be achieved.Although PID-like algorithm is much simpler,the flexibility and quick response ability to deal with the changes of the system state are greatly reduced.Therefore,the adaptive adjustment method proposed in this thesis is superior.(3)Finally,the designed adaptive PID and adaptive PI control algorithm are applied to the second-order nonlinear system model of the train.Through simulation,we can see that the designed algorithm can achieve good tracking control of the speed and displacements,which further the effectiveness of the algorithm.