Multiple Horizon Model Predictive Flight Control

Abstract

T HE analysis and control of various multiple-input multipleoutput (MIMO) systems have been well examined. In many of these systems, the activity and response of various outputs act over different time scales. One such example is an aircraft, where there exist specific inputs that drive certain outputs, allowing the aircraft to maneuver. These various outputs, however, tend to react over different periods because they are affected differently by each input and are often coupled. Controlling one output with an input at a specific rate to obtain a desirable responsemay not necessarily lead to a desirable response in another coupled output. Naturally, certain outputs may need to be managed at higher rates than others to maintain adequate levels of performance. Model predictive control (MPC) allows for an effective method of controlling MIMO systems where significant control coordination is needed to obtain a desired response. MPC is a form of control that uses a model of a particular system to obtain an optimized set of control actions to force the system to a desired reference condition. 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. A detailed summary of MPC and its associated benefits is presented in [1–3], ranging from stability and optimality issues of various MPC formulations to tuning parameter allocations and discretization effects. The primarymethod of regulating the nature of the output response is through the prediction horizon, which defines how far into the future the system is to “look ahead” from its current state to determine the optimal course of action in the future. The length of the prediction horizon itself has a significant effect on the closed-loop behavior. If the prediction horizon is short, then the optimized control sequence will be aggressive to minimize the error between the current state and the desired reference condition. If the prediction horizon is long, then the control inputs will be weaker, allowing for a long-term transition of the system toward the desired condition [2]. CertainMPCmethods [4,5] apply a single, global prediction horizon to the system,meaning that each output is being controlled equally, regardless of the output’s nature. From this perspective, it seems that using a prediction horizon that may be effective in controlling one output may be less than effective at controlling other outputs. Using a single global prediction horizon for MIMO processes may therefore seem impractical for MPC problems. A potential solution is to adopt a multiple prediction horizon strategy that allocates individual prediction horizons to the outputs that are being controlled. The prediction horizons for each tracked output can be tuned to operate within time scales specific to the output. The resulting controller will therefore be able to control that output within the limitations of the system, without greatly affecting the behavior of other outputs. The multiple prediction horizon case for a multivariable system has been considered in [6] with respect to continuous-time generalized prediction control and in [7] with respect to block model predictive control. Applications of variable prediction horizons to aMIMO system are also addressed in [8] relating specifically to spacecraft control. Recent advances in predictive control have led to its implementation onto aerospace systems [8–13] as well as unstable systems [14,15] and have provided more reliable methods of controlling models with nonlinear properties and constraints. The use of multiple prediction horizons becomes particularly useful when attempting to control systems with high degrees of cross coupling between outputs with multiple degrees of freedom. In such cases, having prediction horizons specific to certain tracked outputs may allow for a certain level of decoupling to be achieved, where the response of a particular output can be adjusted without greatly affecting the response of other tracked outputs. This Note develops a general multiple horizon predictive control scheme extending the Algebraic Model Predictive Control (AMPC) algorithm in its application to flight control discussed in [16]. This Note discusses briefly the structure of the AMPC algorithm for a global prediction horizon case, then extends the formulation to accommodate formultiple prediction horizons forMIMO systems. A brief discussion on the formulation of the optimal controller will be given for both constrained and unconstrained cases, followed by a detailed analysis of the application and effect of the multiple prediction horizon method on a highly coupled linear longitudinal aircraft model.