Adaptive control using a moving window Newton-Raphson parameter identification scheme

Abstract
This paper will describe an adaptive control system for aircraft that is based on a parameter identification on-line scheme. The adaptive mechanism uses two elements: one, a digital batch processing of a data record to obtain identified parameters; and, two, algebraic relations specifying the control law constants given the identified parameters. Concerning the first, a data record representing a time history of the most recent state measurements serves as the input to a computational algorithm for the identifier. It has a finite length and, hence, as new measurements are taken, old ones are pushed out of the data batch. The computational algorithm used to identify the parameters is a modified Newton-Raphson scheme. It uses a linearized model to represent vehicle motions. The model is obtained from continuous-time representations of the aircraft dynamics. The continuous-time representation is converted to a discrete form necessary for the model using a first-order Euler integration scheme. The model contains 10 parameters which are to be identified. Three parameters relate to the longitudinal motions of the vehicle and the remaining ones relate to the vehicle's lateral motions. The longitudinal and lateral model parameters affect only longitudinal and lateral model variables, respectively. This permits identification of longitudinal or lateral parameters as subsets when the data record does not contain adequate information for complete identification of all subsets of the model parameter space. Parameter subsets are altered only after a successful test of the rank of the information matrix related to that subset. The second element involves taking the parameter estimates and adjusting control law constants. That operation should be performed only after the process is converged to proper estimates of the parameters. Hence, another test (related to smallness of the model fit error over the data batch) is made to insure that the parameter estimates are meaningful. The design criterion for control law adjustments, given the parameters, is based on maintaining uniform linear response characteristics. Results of tests of the overall system will be presented. The tests are made on a fixed base, six-degree-of-freedom, piloted simulation of the F8-DFBW aircraft. The simulation is resident on the CDC 6600 real-time computer facility at Langley Research Center. The control system is resident on a computing system external to the 6600 facility, an EAI Pacer digital computer system. Control is scheduled using real-time interrupts; but, the processing of the adaptive mechanism is treated as a background job for the system. Records indicating performance of the identifier over a large range of flight conditions will be presented. Results will be presented for different data batch sizes (number of points) and densities (spacing in time between points).

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