A FUZZY LOGIC BASED MULTIPLE REFERENCE MODEL ADAPTIVE CONTROL (MRMAC) By Sukumar Kamalasadan, Adel A Ghandakly Khalid S Al-Olimat Dept. of Electrical Eng. and Computer Sci., Dept. of Electrical and Computer Eng., The University of Toledo, Toledo, OH Ohio Northern University, Ada, OH 16 th International Conference on Computer Applications in Industry and Engineering (CAINE-2003) Sponsored by International Society for Computers and Their Applications(ISCA) 11 th Nov 2003

Abstract Proposing A Fuzzy Scheme for switching Multiple Reference Models within the MRAC framework –Following a rule base, the scheme effectively monitors drastic changes in plant operating conditions –Reference Model switching is performed every time instant based on the plant auxiliary measurements The proposed scheme is computationally feasible and efficient It can be performed online and is well suitable for multimodal systems It provides an interactive multiple model environment with soft switching The proposed scheme is applied to an example system with distributed model parameters to show its effectiveness

Control of Multi Modal Systems (s.a Aircraft, Robotic Arm) is difficult as the system changes its operating mode arbitrarily Controller Properties: It should be dynamic in nature Efficiently respond to the system changes Keeps track of uncertainties Accordingly, generates appropriate control The Classical MRAC FrameworkMRAC Our Multiple Reference Model Adaptive Controller (MRMAC) FrameworkMRMAC –Select a set of Reference Models suitable for the system at different modes –Modes can include normal parametric variations, external disturbance or both –Depending on certain schemes best suitable Reference Model at each time instant is switched and control action is carried out Introduction

Heuristic based Reference Model generation Performs switching of the Reference Model at each time instant with respect to the plant variation Provides a smooth change in the functional relation between the two Process is accomplished keeping track of the plant auxiliary measurements Main idea is to change the Reference Model so that it improves the overall performance in the form of perfect tracking Our Proposed Fuzzy MRMAC Approach

The MRMAC Concept Multi Modal Domain –Let the system be characterized by ‘n’ Reference Models –Let these Reference Models fits in the parametric space ‘S’ –‘n’ Reference Models can be thought of representation of ‘n’ subspaces in the predefined domain ‘N’ –Suppose the plant change is fully captured by these reference models pertaining to the domain ‘N’ –If any one reference model can describe the ideal plant characteristic fully at any instant - Subspace is called “Hard Partitioned” –Real system often exhibits transition from one subspace to another

The MRMAC Concept −Predefined subspaces or modes switching fully from one to another is not advisable −Need arise to smoothly change the reference model defining a trajectory movement along with the plant dynamics in order to effectively control the plant −Effective along the imaginary boundaries of the subspace where hard switching from one reference model to another can deteriorate the system performance −Heurstic based Multiple Reference Model Adaptive Control performs better when compared to a single reference model adaptive control

A set of predefined Reference Models with suitable structure which models the plant for a specific domain of interest An effective switching scheme, which smoothly provides transition between these Reference Models keeping track of the plant change A robust adaptive control scheme, which tunes and provides control at each reference model subspace The main Components of MRMAC

Objective –Control of Complex systems which is affine, “ Multi Modal” and shows sudden parametric ‘Jumps’ Features –Heuristic Based Multiple Reference Model Adaptive Controller –Mitigating the issue related to the computational complexities inherent in existing mathematical methods. –An interacting individual models due to soft switching unlike hard switching algorithms The proposed Scheme Objective and Features

Determination of the Multiple Reference Models Developing a switching mechanism to switch these Reference Models online based on plant auxiliary measurements. Use a stable Direct Model Reference Adaptive Control (MRAC) approachModel Reference Adaptive Control The Design Approach

Overall Scheme : Ref. Model 1 Ref. Model 2 Ref. Model n Command Signal Control Signal Aux. Measurements y Regulator Parameters Error Fuzzy Logic Switching Scheme (FLSS) Output + RegulatorPlant Adjustment Mechanism -  yRyR

An example Investigation A second order Test System is used for investigation under three mode changes The Test System : 1/(s 2 +3s-10) Mode 1 :- 1/(s 2 +30s-10) Mode 2 :- 1/(s 2 +3s-20) Mode 3 :- 1/(s 2 +9s-30) The RM that worked best with the original Test System :- 5/(s 2 +10s+25) The RM that worked best during transition between each mode :- 5/(s 2 +4s+4) TimeT <40T<70T<100 Plant Structure1/(s 2 +30s-10)1/(s 2 +3s-20)1/(s 2 +9s-30) Best RM5/(s 2 +4s+4)

Results comparing output tracking error

Expanding the Test Domain Three cases are generated each with three modes of plant change Table below shows the plant Multiple Modal changes for these cases TimeT <40T<70T<100 Plant Modes1/(s 2 +30s-10)1/(s 2 +3s-20)1/(s 2 +9s-30) Plant Modes1/(s 2 +9s-30)1/(s 2 +30s-10)1/(s 2 +3s-30) Plant Modes1/(s 2 +18s-10)1/(s 2 +24s-10)1/(s 2 +9s-30) Case I Case II Case III

An example Fuzzy Logic Scheme A fuzzy system knowledge base is created for complete operating domain selecting the appropriate best RM’s Proposed fuzzy logic switching scheme has two inputs, two outputs and nine rules The rule base for the case study consists of three input linguistic terms in the form of Small(S), Medium(M) and Large (L) The input values are taken directly as plant parameter values In physical process these linguistic inputs will be the plant auxiliary measurements

An example Fuzzy Logic Scheme The output values are reference model parametric changes directly There are nine rules which generates two output values Min Operation implication method and centroid deffuzzification method has been employed to generated crisp values Table below shows the rule base

Input Output Mapping and Overall Fuzzy Scheme

Input and Output Membership functions

Simulation Results: Case 1 In this case system modes are changed at different time instants as in Table below Fuzzy Logic switching of the RM was performed online at every time instant Table below shows the plant modes and fuzzy RM structure Output error between controller with the best single RM ( the one shown before) and fuzzified RM is compared TimeT <40T<70T<100 Plant Structure1/(s 2 +30s-10)1/(s 2 +3s-20)1/(s 2 +9s-30) Reference Structure By FLSS 5/(s s+1.74)5/(s s+4.11)5/(s s+4.95)

Simulation Results: Case 1

Simulation Results: Case 2 In this case system modes are changed at different time instants as in Table below Fuzzy Logic switching of the RM was performed online at every time instant Table below shows the plant modes and fuzzy RM structure Output error between controller with the best single RM ( the one shown before) and fuzzified RM is compared TimeT <40T<70T<100 Plant Structure1/(s 2 +9s-30)1/(s 2 +30s-10)1/(s 2 +3s-30) Reference Structure By FLSS 5/(s s+4.95)5/(s s+1.74)5/(s s+6.32)

Simulation Results: Case 2

Simulation Results: Case 3 In this case system modes are changed at different time instants as in Table Fuzzy Logic switching of the RM was performed online at every time instant Table shows the plant modes and fuzzy RM structure Output error between controller with the best single RM ( the one shown before) and fuzzified RM is compared TimeT <40T<70T<100 Plant Structure1/(s 2 +18s-20)1/(s 2 +24s-10)1/(s 2 +9s-30) Reference Structure By FLSS 5/(s s+4.93)5/(s s+1.74)5/(s s+4.94)

Simulation Results: Case 3

Concluding Remarks A Multiple Reference Model Adaptive Control scheme with online Fuzzy Switching is proposed for plants with multimodal changes The scheme is very effective and computationally efficient for reference model switching Proposed scheme provides ‘soft' switching of the reference models, especially at the modal boundaries The scheme can be used for scheduled switching in which certain auxiliary measurements are monitored to keep track of unforeseen changes in the plant operating mode With the help of additional learning strategy the rule based switching can be modified online thus expanding the operating range The scheme can be effectively used as an Intelligent Controller for highly dynamic and functionally uncertain systems such as aircraft control

Multi Modal Domain Predefined Domain ‘N’ Subspace ‘b’ Subspace ‘a’ ……. :::: Subspace ‘n’

Develops a Control Law looking at the Input and Output of the Plant Updates the Control law using an Adaptive Mechanism Use a reference model to effectively model the dynamics and forces the plant to follow that model MRAC Structure