미지의 외란과 잡음을 받는 확률시스템의 상태추정과 제어

Abstract

Abstract

PID controllers have been widely used in lots of industrial fields because of several positive characteristics. Its structure is so simple to implement and to apply, while its control performance is higher than those of other type controllers for linear time invariant systems. Especially, PID control technique is very useful and effective as long as the given controlled systems are deterministic without any types of noises.

By the way, the real systems found in industrial fields are under noisy circumstance including RMS and/or random noises, and thus they are used to be mathematically modeled as linear time invariant stochastic systems. Although the effect of RMS sinusoidal noises can be reduced by way of comprising a kind of filter such as an RC filter, the effect of random noises can not be reduced by filters.

Under noisy circumstance, the D control action of all types of PID controller, for example conventional PID or fuzzy PID, may not be operated normally in steady state by the influence of noises. As a result, the output of PID control systems often exhibits a chattering phenomenon around the given reference input in steady state.

When a set of unknown disturbances is driven for the controlled system, even the PID control system may not track the reference input and may resultantly exhibit a steady state error.

In order to improve the wrong D control action by the effect of noises, in this paper, a method to comprise PID control system by adopting the separation principle is suggested. A procedure to comprise the controller according to the suggested method by the separation principle is as follows: At first, the state of the PID control system is estimated by the Kalman filter algorithm using the noisy output under the assumption that the system and measurement noise of the PID control system should be white Gaussian random noises. And then the estimated output from the Kalman filter is fed back to the PID controller to generate an error signal.

In order to compensate the effect of the unknown disturbance, in this paper, a method to comprise PID control system based on Kalman filter with an unknown disturbance estimator is suggested. The used unknown disturbance estimator is composed based on the fuzzy estimation algorithm. When the unknown disturbance is estimated, the estimated value is fed back into the Kalman filter algorithm to compensate the filtered state and fed back into the PID controller to generate a new control input for the purpose of reducing the steady state error of the PID control system.

The eventual PID controller structure to improve the D control action against noises and to compensate the effect of unknown disturbance is suggested, by combining the fuzzy PID controller with Kalman filter based on the unknown disturbance estimator.

In order to verify the control performance of the suggested control system, several simulations were accomplished under circumstances with noises and/or unknown disturbance. As a result, the comprised control system exhibited very good control performances for all simulation conditions and conclusively the effectiveness of the suggested method was qualitatively verified.