A PID Neural Network Controller Pan Pan 2005.05.20

Agenda-- Introduction The structure and function of PID neural network Structure of fuzzy PID controller BACK-PROPAGATIAON algorithm of PIDNN Simulation results Conclusion

Introduction Conventional proportional-integral-derivative (PID)controllers are well known and have been extensively used for industrial automation and process control for about half a century . However, conventional PID controllers generally do not work well for time-delayed linear systems, nonlinear systems, complex and vague systems. The fuzzy PID controllers are designed for this purpose. Fuzzy controllers have been successfully implemented for many linear and nonlinear processes, even sometimes they are proved to be more robust than conventional controllers. The natural representation of control knowledge make fuzzy controller easy to be understood. But the fuzzy controller with two inputs, error, the change rate of error, approximately behaves like a PD controller, and obviously there would exist steady-state error when industrial process systems are controlled by conventional fuzzy controller.

Introduction In order to improve further the performance of the transient state and the steady state of fuzzy PID controller, several optimum or near optimum solutions are developed, such as training algorithm using input/output data, genetic search algorithm , peak value tuning method for fuzzy PID controllers. These methods regulate the parameters of membership function and the parameters of PID structures. They provide better functional properties efficiently. A PID neural network (PIDNN) also is an optional method is given to make the performance better

The Structure and Function of PID Neural Network PID neural network is a kind of neural network that consists of P neuron, I neuron and D neuron, where P neuron possesses proportional operation function, I neuron performs integral function, D neuron carries out derivative function. In order to provide input channels for input values and feedback values, PID neural network adopts 2-3-1 topology with three Layers shown in figure.

Structure of Fuzzy PID Controller It is difficult to obtain control rules with the input variable sum-of-error e, that is integral error, because the steady state value of integral n error is unknown for various control systems. So the one-input (error e) or two-inputs (error e and error change e) fuzzy controllers are common and conventional one in various application. It stands to reason that fuzzy PID controllers are constructed with one-input or two-inputs.

Fuzzy PID Controller

PID Neural Network

BACK-PROPAGATIAON algorithm of PIDNN The back-propagation algorithm of PID neural network is a analogous algorithm for conventional forward neural network. It is one of the important methods to optimize the weight value of forward neural network. The learning structure of PID neural network is shown in figure.

Simulation Results The first example is the first order systems with the simple model as follow:

Simulation Results The second example is the second order system. The model of it is obtained as following

Conclusion A fuzzy PID controller with PIDNN is a discrete-time version of PID controller’combined fuzzy controller with PID neural network. The controller has adaptive control capability and optimized via the back-propagation algorithm. The results demonstrate that fuzzy PID controller with PIDNN has much better performance than conventional one.