ESA GNC Conference Papers Repository

A Low-Order Linear Parametric Varying H infinity Loop-Shaping Controller for a Re-Entry Vehicle
Menon, P., Prempain, E., Postlethwaite, I., Bates, D.G.
Presented at:
Tralee 2008
Full paper:

It is common practice in the space industry to obtain a global nonlinear controller by scheduling certain gains of a set of local linear controllers. The local linear controllers are designed for linearized models of the nonlinear system at several different operating conditions. Though this approach is conceptually straightforward, the methodology is rather ad-hoc and comes with no theoretical guarantees in terms of robust stability and performance. Hence, the amount of time and effort required in order to validate the resulting design may be extremely large. To address this problem, a certain amount of research effort has been expended in recent years in an attempt to introduce a more theoretically rigorous framework for gain scheduled controller design, by explicitly considering the scheduling variables at the time of synthesis. The result of this research effort has been the so-called Linear Parameter Varying (LPV) controller design methodology, [1-6]. One particular variant of the standard LPV approach, which appears to have strong potential for real industrial application, is the recently developed LPV loop shaping design procedure, [8-12]. In this procedure, the LPV plant is augmented with weighting functions at the input and output, in order to shape the open loop singular values according to classical design principles, e.g. high gain at low frequencies, low gain at high frequencies, and a moderate roll-off rate around the unity gain crossover frequencies. A full-order [11,12], or static, [9,11], output feedback controller is then computed using standard LMI optimisation for the augmented LPV plant. In this paper, a low-order LPV loop shaping controller, which employs a static output feedback compensator, is developed and applied to the problem of controlling the lateral-directional dynamics of a model of the X-38 re-entry vehicle [13,15]. In this model the state vector consists of sideslip angle, roll rate, yaw rate and bank angle, while the aileron and rudder control surfaces are used for control purposes. Both actuators are modeled as second-order critically damped transfer functions with a natural frequency of 26rad/sec. The linearised models of the X-38 at three different flight conditions (subsonic Mach = 0.64, transonic Mach = 1.05 and supersonic Mach = 2.38), along the nominal trajectory are used to construct the polytopic representation of the system [3,9]. The resulting design is shown to be easy to tune, comes with extremely strong robustness guarantees, and should be relatively straightforward to implement in real-time. A comparison of the performance of our low order LPV controller against the NDI design reported in [13], indicates that the proposed approach has the potential to significantly outperform much mnore complicated designs.