# Optimal Input Design for Aircraft Parameter Estimation using Dynamic Programming Principles

Abstract: A new technique was developed for designing optimal flight test inputs for aircraft parameter estimation experiments. The principles of dynamic programming were used for the design in the time domain. This approach made it possible to include realistic practical constraints on the input and output variables. A description of the new approach is presented, followed by an example for a multiple input linear model describing the lateral dynamics of a fighter aircraft. The optimal input designs produced by the new technique demonstrated improved quality and expanded capability relative to the conventional multiple input design method.

## Summary (1 min read)

### Introduction

- Aircraft flight tests designed specifically for the purpose of parameter estimation are generally motivated by one or more of the following objectives: 1. The desire to correlate aircraft model parameter estimates from wind tunnel experiments with estimates obtained from flight test data.
- The fundamental principles and procedures regarding the input design remain unaltered.
- Comparisons using the Cramer-Rao bounds isolate the merits of the input design from the merits of the parameter estimation algorithm used to extract the aircraft model parameter estimates from the flight data.
- Global minimization of the required flight test time, subject to the conditions of the problem formulation, so that results from expensive and limited flight test resources can be maximized.

### 5. Single pass solution.

- The next section describes the problem formulation.
- Following this is a description of the solution method which uses the principles of dynamic programming.
- Several example input designs using the new technique for the lateral dynamics of a fighter aircraft are then given.

### Problem Statem&

- For aircraft parameter estimation experiments, typically a linear perturbation model structure is assumed.
- The flight test inputs are perturbations about trim to ensure that the system response can be adequately modelled by such a structure.
- Practical input constraints, including maximum input amplitudes, control system dynamics, input spectrum high frequency limitations, and, in cases where a human pilot must realize the designed input, pilot implementation and coordination constraints.

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