Online Tuning of the Fuzzy PID Controller using the Back-Propagation Algorithm
Abstract
This paper presents a novel methodology for the online update the fuzzy rule base of the type-1 fuzzy logic system that estimates the proportional-integral-derivative (PID) gains of the professional PID control. Two different types of benchmarking PID controllers are used to compare the performance of the proposed methodology. The first controller is the so-called professional PID (P-PID), where the proportional gain KP, the integral gain KI, and the derivative gain KD, are offline calculated based on the dynamics of the process under control using the Zeigler Nichols method: in this controller the three gains remains fixed during the entire process control. The second controller uses three type-1 fuzzy logic systems to estimate each one of the gains of the professional PID controller every control cycle; each fuzzy rule base is offline estimated by the expert and remains fixed during the complete control process. This paper proposes a fuzzy self-tuning professional PID controller: it has three singleton type-1 fuzzy logic systems to calculate each gain of the controller every control cycle, with the novel characteristics that each fuzzy rule base is updated and tuned each feedback cycle using the back-propagation BP algorithm. This proposal is named the fuzzy professional proportional-integral-derivative controller (T1 SFLS P-PID) with back-propagation (BP) tuning. The experiments show that the proposed fuzzy self-tuning controller has better transient performance compared with the two benchmarking controllers. It shows the minimum overshoot and the minimum response time.
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Introduction
In [1] a fuzzy PID controller is used to reduce the overstress that arise in the actuators so as improve in a considerable way the speed of response. The work done in [2] considers different variables that influence directly or indirectly in the process by which different types of controllers are implemented to counter the effects of these variables. In some cases, it chooses to implement a fuzzy proportional and derivative controller to decrease the overshooting and the period of time, and a fuzzy integral controller is used as a switch for selecting the best response signal. The control the speed of motors using PID and T1 SFLS PID controllers is presented in [3]. The usage of a T1 SFLS PID controller based on two fuzzy logic controllers (FLC) acting as inputs, wher the PID gains are calculated using the Ziegler-Nichols [4], [5]. It can use the simulation to make comparisons between a classic PID controller and a T1 SFLS PID controller, and also evaluate the results of both controllers and observe the differences between them, the differences that often occur between these systems are better signal response, higher reaction rate and thereby the system performance is improved. A control of a single process that uses a T1 SFLS PID and a type-2 SFLS PID is presented by [6]. In this case, three different PID controllers are obtained using a genetic algorithm (GA), named linear PID controller, T1 SFLS PID, and type-2 SFLS PID.
The type-2 SFLS PID offers the best control for the application. The work done in [7] proposes a type-2 FLC to control the position of an actuator in order of few milimeters, and uses the parameters with uncertainty. In [8] an interval type-2 SFLS PID controller with two inputs and one output is used for switching control.
This paper presents a T1 SFLS P-PID controller that online updates the rule base of each gain using the BP algorithm. For the best knowledge of the authors there is not publication reporting the proposed mechanism.
The paper is organized as follow. Section 2 gives the foundations of PID controllers. Section 3 explains the proposed methodology. Section 4 presents the results of the test experiments, and the Section 5 summarizes the conclusions.
Conclusion
According to the experimental results, the T1 SFLS P-PID-BP presents the better performance in comparison with the two benchmarking controllers, the P-PID and the T1 SFLS P-PID controllers. This was achieved because of the implementation of the mechanism to update the fuzzy rules. The overshooting of the behavior of the controlled plant is eliminated, and the velocity of the response is faster.