Design of robust sliding mode controllers for missiles with unmatched uncertainty

Abstract

To improve the performance of the classical three-loop autopilot, the thesis deals with approaching the missile autopilot process from a sliding mode control (SMC) perspective. A major difficulty of SMC for missile acceleration control comes from the fact that missile acceleration dynamics are non-minimum phase, because SMC is generally not feasible for systems with non-minimum phase. To overcome this difficulty, several authors have proposed so-called combined topology SMC where the matching conditions are satisfied. The basic idea of the combined topology SMC for missile acceleration is to employ minimum phase controller with an additional acceleration loop. However, the topology is more complicated and the introduction of observer into an angle-of attack sliding mode controller can easily destroy the insensitivity properties. In this thesis, we propose a guaranteed cost SMC as a new design of missile acceleration control where we partially give up the matching conditions in return for designing the sliding surface in the form of classical three-loop topology. Because the matching condition of uncertainty is not satisfied, sliding surface choice becomes crucial. In addition, gain selection schemes, based on optimal control theory, are presented to extend SMC by incorporating the new techniques. The reason for incorporating the gain selection schemes is to retain the main advantage of SMC and also yield more robust or desired performances. The VSGCC is presented to incorporate a guaranteed cost control (GCC) scheme for robust performance and the VSOCC is, on the other hand, presented to incorporate an optimal cost control (OCC) scheme for optimal performance.

Specifically, to implement the guaranteed cost SMC, we present a state feedback sliding mode control topology, which is named as a variable structure three-loop controller (VS3LC). Being different from output feedback sliding mode control topologies, the VS3LC does not provide system invariance to all the uncertainties, but has an advantage in implementation because it needs the same information as the classical thee-loop design except an additional term for robustness improvement. Combination of the VS3LC and GCC gain selection scheme construct the sliding surface such that the sliding motion satisfies a $H_∞$ criterion. The GCC ensures the sliding motion to be stable under the unmatched uncertainties by providing an upper bound on a performance cost otherwise the sliding motion may become unstable or performance may degrade. While being affected by unmatched uncertainties, the sliding motion goes with robustness properties against unmatched uncertainties due to advantages of the GCC schemes.

The OCC is a newly proposed gain design procedure based on optimality condition. Note that optimal controller, based on optimal theory, is only optimal with respect to the prescribed cost function and does not necessarily represent the best controller in terms of the usual performance measures used to evaluate controllers. To minimize the cost function and achieve desired pole placement at the same time, we have derived an expression to relate the weight parameters appearing in the performance cost to the design parameters. By substituting corresponding parameters into the expression, required performance cost for optimal control is inversely calculated without the need for design weight adjustment. The optimality criteria for the three-loop autopilot are derived to find out all set of design parameters for which the control is optimal. Based on the criteria, a new gain design procedures are presented where time constant is set to design objective and open-loop crossover frequency and phase-margin as design constraints. Combination of the VS3LC and OCC gain selection scheme will allow us to provide a switching surface with stable dynamics and the cost minimization interpretation. The effectiveness of the proposed schemes is illustrated through numerical simulations.