Optimal Control Based Flight Control Law Clearance Using Generalized Polynomial Chaos

In this paper we consider the application of generalized polynomial chaos (gPC) methods for uncertainty quantification in the context of optimal control based flight control law clearance using quasi-linear models. The closed loop aircraft model is assumed to be linear and may be obtained from linearization in a reference flight condition. In addition, nonlinear effects related to actuator rate and position limits are introduced in the analysis, which are crucial for the investigation of worst case inputs. For the presented approach the plant is modeled as uncertain, that is the system matrix depends on uncertain parameters subject to a distribution. Under this type of modeling, stochastic moments of the linearized worst case criterion can be obtained using gPC with a stochastic collocation approach. The example problem considered in this paper investigates the maximum load factor under worst case pilot inputs in the longitudinal plane including rate and position saturations for the elevator servo. In this example, the uncertain plant depends on distributed parameters for pitch damping and pitch stiffness. The mean and standard deviation of the criterion are computed based on the gPC method. The comparison of the results to a Monte Carlo analysis show rapid convergence and excellent correspondence with the values of the estimated stochastic moments. In particular, the presented approach for uncertainty quantification of the criterion under worst case pilot inputs requires only a fraction of the samples needed for standard Monte Carlo analysis.     «

In this paper we consider the application of generalized polynomial chaos (gPC) methods for uncertainty quantification in the context of optimal control based flight control law clearance using quasi-linear models. The closed loop aircraft model is assumed to be linear and may be obtained from linearization in a reference flight condition. In addition, nonlinear effects related to actuator rate and position limits are introduced in the analysis, which are crucial for the investigation of worst c...     »