Efficient Model Predictive Control Algorithm for Aircraft

Abstract

M ODEL predictive control (MPC) has received much attention since its development over 40 years ago. Within the past 20 years, its application has steadily grown and is now in widespread use, particularly in the process industry [1] using systems with slow, predictable properties. Recent advances in predictive control have lead to its implementation onto faster dynamics systems [2,3] and unstable systems [4], providing amore reliablemethod of controlling models with nonlinear properties and constraints. There has also been significant research into the use of MPC in aerospace applications. These include addressing issues of robustness [5], model reduction to minimize computational demands [6] and application into airborne platforms [7]. The aim of MPC is to determine, online, an optimal control sequence that minimizes the cost of reaching a reference condition within a given prediction horizon given knowledge of the system and current state information. MPC can therefore be considered more effective than other control strategies, as it not only attempts to minimize past and current errors, but also considers the effects of future errors. A detailed summary ofMPC and its associated issues is presented in [8,9]. The use of state-space models has gained increased attention for their ability to easily and accurately control multivariable processes within an MPC framework [10]. Existing formulations of predictive control using state-space models such as generalized predictive control (GPC) [11] among others rely on the discretization of the system over a fixed period to formulate a suitable discrete state-space model. This discretization period ultimately defines the interval over which the predicted samples are calculated, with the prediction horizon defined as the number of discrete steps into the future the system is to observe [12,13]. To retain model accuracy, the discretization period is kept small in order to model all possible system dynamics. However, small discretization periods, although good for model accuracy, results in poor computational performance as an increased number of samples are needed to observe future outputs for a given prediction horizon. This restricts the applications of MPC into fast dynamic systems (which require small discretization periods to capture all system dynamics), as the online computational burden is too great. If the discretization period was made larger to improve computational performance, the algorithm risks being unable to model fast model dynamics and in some cases, destabilizes the closed-loop performance. Formulations such as those discussed in [14] use continuous-time versions of GPC to control multivariable systems by predicting over specific time intervals as opposed to a fixed number of discrete steps to improve prediction accuracy computational efficiency. This Note introduces a method of MPC using variable prediction time intervals to reduce the level of computation required without losing model accuracy, based on models formed using the eigenvalues/eigenvector characteristics of the system. This Note discusses in detail the formulation of an algebraic model predictive control (AMPC) algorithm using fewer prediction points to generate smaller prediction matrices. An analysis of the controller on a linear longitudinal aircraft model will be performed using a variety of controller configurations, assessing the effectiveness and controllability of the system using the proposed AMPC formulation compared with standard MPC formulations.