Constrained Multi-objective Optimisation of a Controller for a Highly Nonlinear Aeroelastic Structure—testbed Design

The need for weight-optimised aerospace structures results in flexible structures with highly nonlinear behaviour. Their control presents challenges that require control theory be developed in order to enable the trend toward lighter structures to continue. Two classes of problem of particular interest in control are systems with a high degree of nonlinearity inherent in the structure and those with nonlinear and noncontinuous external forces. These are represented respectively by space structures and those subject to aeroelastic effects. The problem of control of highly flexible space structures have previously been considered by the author (Drack, Zadeh, Wharington, Herszberg and Wood, 1999; Zadeh, 2002). Optimal control of a two dimensional aeroelastic (wing) structure with three degrees of freedom is considered. Due to publication space limitation, results are presented in two papers; this and a follow-up paper (Zadeh, 2005). INTRODUCTION Weight is of primary concern in aircraft design, affecting all performance indicators, with the extensive use of composite materials being testimony to this. In special application aircraft, such as those intended to operate at very high altitude with very low wing loadings, the wing becomes a high aspect ratio, lightweight, flexible structure. The ability to produce a lighter structure that is immune to the potentially destructive effects of aeroelasticity is thus very desirable. Although conventional control theory is reasonably wellestablished and mature, it is mainly limited to rather simple applications. Control of aeroelastic behaviour of aerospace structures pose various challenges which limit the usefulness of conventional control techniques. The characteristics common to these class of applications are: • there usually exist high number of hidden or unobservable states, making the use of state estimators difficult. These include aerodynamic states, and structural bending and torsional states. • these systems are highly nonlinear, limiting the applicability of conventional state space techniques. For example, aerodynamic loads are nonlinear and sometimes even noncontinuous. • these structures are difficult and very expensive to test. Controllers needed in aerospace applications usually needs be optimal with respect to multidisciplinary criteria and a variety of potentially conflicting constraints, as well as being robust with respect to system parameter variations and uncertainties. Fuzzy Logic Control (FLC) is considered as a nonconventional control stratagem for designing control systems that can cater for system nonlinearities and discontinuities (MathWorks Inc., 1994). FLCs are usually designed by providing expert input to the controllers in the form of linguistic phrases (Wang, Mo and Chen, 1995; MathWorks Inc., 1994). Expert advice can thus be intuitively implemented, however, the resulting FLC is a nonlinear and potentially discontinuous transfer function that maps input(s) to output(s). Furthermore, this method of control design can also result in sub-optimal controller performance. Conventional control techniques usually cannot be applied to design of FLCs, as they are, by their very nature, nonlinear. Therefore, FLC design methodologies require either handtuning or numerical optimisation in order to achieve superior or robust performance. Such diverse performance requirements could mean that if such performance is showed to be satisfied on the test problems, there is some evidence that the methodology will be applicable to broader classes of problems. The optimiser required for this task must be capable of handling many local minima, and be able to achieve a good result on current computing hardware in a reasonable period of time. Simulated annealing (Kirkpatrick, Gelatt Jnr. and Vecchi, 1983; Ingber, 1993) is used in this research in place of calculus based optimisation techniques in order to overcome the above difficulties. This paper is organised into a number of sections. Aeroelastic instability is explained in the next section, followed by definition of the research problem. The aeroelastic testbed, and design of a nominal fuzzy logic controller are then covered. Simulation methodology and simulation results of the nominal controller are presented. The nominal controller has been used as the basis for designing an optimised controller using a constrained, multicriteria, stochastic optimisation scheme. Because of publication space limitations, the optimisation of the controller has been submitted as a separate, follow-on, publication (Zadeh, 2005). CONTROL OF AEROELASTIC SYSTEMS Aeroelastic phenomena occurs due to a combination of inertia, aerodynamics, and elastic forces (Figure 1). Aeroelasticity (and particularly aeroelastic instability) did not attain