Integrated fuzzy/nonlinear flight controller synthesis for rotorcraft

Abstract

Introduction In this paper, synthesis of a helicopter full authority flight controller using an integrated (fuzzy) rule based and (nonlinear) model based control approach is presented. First, fuzzy rules, based on qualitative analysis of helicopter response characteristics and choosing the input membership function using genetic algorithm(GA), are developed for converting velocity and acceleration commands in the horizontal plane into required pitch and roll attitudes of the vehicle. Then, a model-based nonlinear controller previously developed for control of body attitudes is combined with the rule-based fuzzy controller to arrive at an integrated fuzzy/nonlinear control approach. Its performance is evaluated through simulation of typical command maneuvers. Also, preliminary results for choosing input membership functions using GA for the combined longitudinal and lateral case are included. The use of nonlinear controller synthesis techniques, such as feedback linearization, for helicopter flight control system design is an alternative to conventional gain scheduling approaches that are based on linearized models [I-41. The main advantage is that the feedback linearization technique results in a single controller valid throughout the flight envelope and hence eliminates the need for gain scheduling. In order to apply this technique, the system under consideration has to be square with respect to its inputs and outputs. Past designs have exploited the natural time scale separation between position and attitude dynamics of the vehicle, and treat the vehicle attitudes as pseudo-command variables [3,4]. These pseudo-command variables are obtained using approximate model inversion [4]. However, the approximations involved in computing the pseudo command may not be valid whenever the control forces are significant in comparison to vehicle accelerations and body forces. Applications of fuzzy logic for helicopter flight control system development have been receiving considerable attention recently [5-71. The main advantage * Copyright 0 1 995 b y the American Institute of Aeronauis that since a fuzzy controller is rule based, it can be tics and Astronautics,Inc. All rights reserved. t ~ s s o c i a t e Professor, senior member of AIAA. easily implemented and modified. Also, in general, t Graduate Student. (404) 853-0173 the need for accurate knowledge of vehicle model dur§Graduate Student, student member of AIAA. ing the design process is eliminated. In this paper, we replace the approximate model inversion scheme used in [4] for generating pseudocommands by a fuzzy logic based inversion scheme. In fuzzy logic design, the fuzzification and defuzzification processes play an important role in determining the effectiveness of the resulting design. The input membership functions used for fuzzification could be tuned so that the closed loop system exhibits certain performance characteristics. However, manual tuning of these functions based on trial and error could be tedious and ineffective. Past studies have used nonconventional optimization techniques, such as genetic algorithm(GA), to tune these membership functions based on certain performance cost [6-91. Optimization schemes, such as GA, are particularly suitable for fuzzy logic design because GAS do not require derivative information and are guided by probabilistic transition rules. Past results [9], using only manual tuning, indicate that the performance of fuzzy inversion model based nonlinear controller design is better than the approximate model inversion based nonlinear controller design. In this study, we employed a GA for generating the input membership functions in fuzzy logic based inversion development [9] using an implicit model following cost function. Simulations were carried out using the modified TMAN simulation model [lo] of the Apache helicopter. This paper is organized as follows: First, we present an overview of the helicopter nonlinear flight control schemes used in the past and the need for implementing the fuzzy scheme. This is followed by a description of the fuzzy module synthesis procedure. Then, we describe the fuzzy inversion scheme used in this study followed by nonlinear simulation, conclusions and recommendations. Helicopter Nonlinear Flight Control Scheme A six-degree-of-freedom rigid body dynamic model of a helicopter is used in this study [4]. A general representation of the six-degree-of-freedom helicopter dynamic equations is given [4] by where x = [X, Y, 2, 0, 4, $IT and 77 = [be, b,, b,, bplT. In (I), be, 6, and 6, are the longitudinal cyclic, collective and lateral cyclic controls of the main rotor, Nonlinear Helicopter Controller Figure 1: Helicopter Model with Nonlinear Inversion Module respectively, and 6p is the tail rotor control. The vector of output variables to be controlled, S, can be written as