Mathematical Problems in Engineering

Volume 2015 (2015), Article ID 386073, 10 pages

http://dx.doi.org/10.1155/2015/386073

## A Novel Online Self-Structuring Fuzzy Control Algorithm and Its Application

Key Laboratory of Electronic Equipment Structure Design of Ministry of Education, Xidian University, 2 Taibai Road, Xi’an 710071, China

Received 22 December 2014; Revised 16 March 2015; Accepted 10 April 2015

Academic Editor: Farhang Daneshmand

Copyright © 2015 Siyuan Feng et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

This paper proposes a novel self-structuring algorithm for the online adaptive fuzzy controller (SA-OAFC). The SA-OAFC capable of adding and deleting inference rules autonomously can start operating with an empty set of fuzzy rules based on the desired output and actual output of the system to avoid conventional differential operation. It also takes advantage of the auxiliary fuzzy system to evaluate the approximated results with little information of the plant. The SA-OAFC is characterized by its good engineering approachability, robustness for all kinds of perturbations of the plant, and the ability to perform variable selection among a group of candidate input variables. Moreover, it manages to remarkably reduce the amount of computation and decrease the complexity of the system. This paper demonstrates the capabilities of SA-OAFC by a simulation example and then hardware-in-the-loop (HIL) experiment.

#### 1. Introduction

With the popularization of artificial intelligence in control field, the fuzzy control has been widely used in recent years [1–3]. However, according to thorough investigation of state of the art of current fuzzy control methods, most of the fuzzy controllers are of fixed structures, except that a few of them have real-time adaptive parameters [4–6]. Under these circumstances, one needs to not only define the rule base and membership functions (MFs) for these fuzzy controllers in advance but also redesign the whole system in case of the changes of the plant or the working condition.

Aiming at this shortcoming, some researchers have proposed the self-structuring fuzzy controller [7–12] where the MFs and rules of the fuzzy system can be increased and adjusted to improve the system structure based on some methods. Park et al. [7] used a method with a fixed width triangular MF, whose MFs and rules increase based on the extended input space. So the input space is divided evenly by the MFs, and there are the issues of the irrational distribution of MFs and the unlimited growth of rules. Cara et al. [11] used the auxiliary fuzzy system to determine the approximate effect of controllers and the positions where there is a need to increase the MFs to achieve a reasonable distribution. But for a complex plant, the unlimited growth of rules still remains, and it is prone to oscillate while the new rules are initializing. To overcome this drawback, Chen et al. [12] adopted the “pseudo fuzzy output” method to determine the initial consequents of the new rules, successfully resolving the oscillation problem and according to the contribution of the rules, they deleted rules to limit the number of rules, but they only removed the redundant rules, ignoring the redundant MFs.

Based on the characteristics of the methods described above, this paper proposes a novel self-structuring algorithm for the online adaptive fuzzy controller (SA-OAFC). In the case of the mathematical model of the plant unknown, this controller starts working online with empty rules and expands the coverage of MFs dynamically depending on the desired output and the actual output of the system, which has the advantages of a small amount of computation, good robustness, and a reasonable distribution of MFs. The main contribution made in this work is designing the SA-OAFC for intelligent control system and testing and analyzing this algorithm by a simulation example and a HIL experiment under disturbance condition.

The rest of this paper is organized as follows. Section 2 presents the control problem to be solved and the structure of the fuzzy controller employed. In Section 3, the proposed SA-OAFC is described in detail. Then, Section 4 shows the simulation results illustrating the main features of the SA-OAFC. Finally, several conclusions are drawn in Section 5.

#### 2. Problem Description

Without loss of generality, we consider the following dynamic plant [13]:where is an unknown continuously differentiable function, is the output of the plant at time , is the control input, and and are unknown constants related to the plant.

The purpose of the controller is to ensure that the output of the plant is able to track a desired signal . As for the general controllers, the structure shown in Figure 1 often requires the differential operation for taking the error and the rate of error as the inputs. But in practical engineering applications, the differential signal is often susceptible to noise which might cause large errors and that is the reason why the proportional-integral (PI) control is applied more widespread than the proportional-derivative (PD) control. Thus, it is assumed that there exists a function such that the control input is given bywhere is employed to avoid differential input signal and make the output of the plant in the next time satisfy . To approximate the function , this paper employs the Takagi-Sugeno (T-S) fuzzy system. The th fuzzy rule is as follows [14]:where and are the crisp input and output of the fuzzy system, are the MFs of the input , is the number of the MFs for that input, and is the consequent of the th rule. Thus, the output of the fuzzy controller is given by [14]where represents the parameters of the fuzzy controller, is the number of the fuzzy rules, and is the activation degree of the th rule.