Rotorcraft Trajectory Tracking Using the State-Dependent Riccati Equation Controller

Abstract

This paper deals with the State-Dependent Riccati Equation (SDRE) method for designing a rotorcraft flight controller. It focuses on the design of the SDRE controller when a highly complex rotorcraft mathematical model is used. The requirements of the rotorcraft model are investigated to design the SDRE controller and to validate the final designs. Since the SDRE method can be applied to a deterministic system, adequate fidelity in the rotorcraft mathematical model is crucial to guarantee controller performance. However, a complex mathematical model generally prevents us from analytically deriving the State Dependent Coefficient (SDC) form of the system equations, which conforms to the basic structure of the SDRE method. This paper proposes a pure numerical procedure for SDC factorization of the motion equation. The numerical methods available to solve the algebraic Riccati equation are selected to cope with the inherent system instability and are applied to the trajectory tracking problems. The overall feature of the present approach is highlighted through analysis of a bob-up and turn maneuver. The results can be utilized as a guide for appropriate selection of rotorcraft mathematical models and numerical methods in designing a robust SDRE controller.

A Comparative Study of Transcription Techniques for Nonlinear Optimal Control Problems Using a Pseudo-Spectral Method

“…, I E n  (3) path constraints, end constraints, initial states, and final states, respectively. [5,6].…”

“…The objective function shown in (1) can be straightforwardly approximated using (4) and the constraints defined by (3) can be satisfied at each of collocation points. As the results of the above approximations, the NOCP defined through…”

“…The pseudospectral (PS) method is a direct collocation method, which generally outperforms indirect methods, owing to their large radii of convergence, and solves nonlinear optimal control problems (NOCPs) with any type of constraint [1][2][3][4]. In a PS method, the collocation points are specially designed to utilize the highly accurate quadrature formulas and the corresponding analysis converges at an exponential rate for problems with a smooth and well-behaved solution [5][6][7].…”

Optimal Output Feedback Controllers for Spacecraft Attitude Tracking

“…Some real‐life applications also have been controlled successfully by implementation of SDRE techniques. These applications include spacecraft attitude control , rotorcraft flight control , and dive plane control of autonomous underwater vehicles .…”

Finding Optimal Controls for Helicopter Maneuvers Using the Direct Multiple-Shooting Method

“…These trajectory deviations are considered when we define a cost function for optimal control problems. The following form of the quadratic cost function with no terminal cost is implemented in this study 14 : The initial conditions for the state variables are specified by the results of the trim analysis because the maneuver considered for this study is initiated from a steady trim condition. Terminal conditions are defined in terms of the target states at the end of a maneuver:…”