Applied Soft Computing 11 (2011) 3441–3450 Contents lists available at ScienceDirect Applied Soft Computing journal homepage: www.elsevier.com/locate/asoc Feedback linearizing indirect adaptive fuzzy control with foraging based on-line plant model estimation Suvadeep Banerjee, Ankush Chakrabarty ∗ , Sayan Maity, Amitava Chatterjee Jadavpur University, Electrical Engineering Department, Kolkata 700 032, West Bengal, India article info Article history: Received 15 April 2010 Received in revised form 26 July 2010 Accepted 3 January 2011 Available online 11 January 2011 Keywords: Indirect adaptive control Fuzzy certainty equivalence controller On-line plant model identification Bacterial foraging optimization abstract The present paper describes the development of an indirect adaptive fuzzy control scheme employing feedback linearizing technique. The scheme proposes the development of a fuzzy certainty equivalence controller for controlling non-linear plants. This controller is designed on the basis of plant parame- ters estimated online at each sampling instant using bacterial foraging optimization (BFO) technique, a stochastic optimization technique, popularly employed in recent times. The utility of the proposed scheme is aptly demonstrated by implementing it to control the level in a surge tank under a variety of reference input commands, where the fuzzy controller could significantly out-perform the corresponding classical feedback linearizing controller and PSO-based fuzzy controller. © 2011 Elsevier B.V. All rights reserved. 1. Introduction Fuzzy logic has served as a tool for control engineering prob- lems, vagueness in natural language and several other concomitant application problems for more than three decades [1–3]. Tradition- ally, fuzzy control is a pragmatic alternative to challenging control field problems since it provides a very simple and convenient method to design non-linear controllers based on the heuristic approach. Irrespective of the source of this heuristic control knowl- edge, the fuzzy controller provides a very user-friendly formalism and interface for presenting and implementing the notions cur- rently established regarding the achievement of high performance control over real-time problems. However, fuzzy controllers, in their basic implementations, possessed some inherent problems [4,5]:- (i) The design of fuzzy logic controllers (FLCs) is prepared in an ad hoc manner so that it becomes quite difficult to decide how the free parameters should be determined to achieve a particular control-level performance. For example, sometimes no a priori knowledge is available regarding the choice of the membership functions and rule base to meet a specific level of accuracy. (ii) Secondly, for the fuzzy controller developed for a nominal plant, unexpected and inadequate performance may result due to unpredictable changes in plant parameters due to presence of noise in control input or reference input and due to some other environmental effects. ∗ Corresponding author. E-mail addresses: sasuan.bee3@gmail.com, chak.ankush@gmail.com (A. Chakrabarty). To sort out these problems, the idea of adaptive fuzzy control emerged, which can produce a minimum performing controller initially for the nominal conditions and can automatically adapt the parameters and/or the structure of the controller in response to the changes of operating conditions and for load disturbances. There are two general approaches to adaptive fuzzy controllers as following: (a) In one approach known as the direct adaptive fuzzy con- trol (DAFC) [1,6–8], the “adaptation mechanism” observes and records the output signals from the plant and accordingly adapts the parameters of the associated controller to achieve a desired performance level in spite of fickle changes in plant behavior. Often the desired performance is achieved by char- acterizing this with a “reference model” and the closed-loop system is made to behave as the reference model will in spite of any changes in the plant. This concept is known as Model Reference Adaptive Control (MRAC). (b) In another general approach known as the indirect adaptive fuzzy control (IAFC) [1,9,10], an on-line plant identification method is incorporated to estimate the plant parameters. Sub- sequently a “controller designer” module is implanted which will determine the parameters of the controller from these esti- mates. If the plant parameters vary, the variation gets reflected in the estimate provided by the identification module and con- sequently the controller parameters will be tuned accordingly in each sampling instant. In this aspect, it can be assumed that the “certainty equivalence principle” is followed, which states that the estimated plant parameters are equivalent to the actual ones at all times. This implies that if the “controller designer” 1568-4946/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.asoc.2011.01.016