Recently, a fully controllable quaternion spacecraft model was proposed. Based on this controllable quaternion model, an analytic linear-quadratic regulator (LQR) design for a spacecraft control system was obtained. Although the LQR design is based on the linearized quaternion model, it was shown that the design of the LQR control system globally stabilizes the original nonlinear spacecraft system. Because in spacecraft design practice engineers normally use models with simplified system dynamics and cost function (which has diagonal structure and excludes external torques) to make the design complexity manageable, this paper will show that the LQR control design is a robust pole assignment design; therefore, the controller is insensitive to the modeling error and external disturbances of nonlinear spacecraft systems. All these properties make this design very attractive. First, the designed controller locally achieves the desired performance because LQR design is optimal for the linearized system and the pole positions determine the critical design parameters such as rising time, settling time, and overshoot percentage. Second, the design is robust to the modeling error because it is a robust pole assignment. Third, the designed state feedback matrix has an analytical form that is represented as a function of the desired closed-loop pole positions or the cost matrices and . This allows convenient tuning of the state feedback matrix to get the desired pole positions and/or balance cost of performance requirements defined by and cost of fuel consumption defined by during the design process. Last, the design globally stabilizes the original nonlinear spacecraft. An example is used to describe the design process, and simulations are provided to demonstrate the desired properties and effectiveness of the design method.
Quaternion-Based LQR Spacecraft Control Design Is a Robust Pole Assignment Design
Journal of Aerospace Engineering ; 27 , 1 ; 168-176
2012-03-28
92014-01-01 pages
Article (Journal)
Electronic Resource
English
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