RECEDING HORIZON CONTROL OF AN F-16 AIRCRAFT: A COMPARATIVE STUDY T. Keviczky and G.J. Balas Department of Aerospace Engineering and Mechanics, University of Minnesota, 107 Akerman Hall, 110 Union Street S.E., Minneapolis, Minnesota 55455 Phone: +(612) 625-8000 Fax: +(612) 626-1558 E-mail: keviczky@aem.umn.edu / balas@aem.umn.edu Keywords: Receding Horizon Control, Flight Control, Opti- mization Abstract A comparison between Receding Horizon Control (RHC) ap- proaches is presented for the longitudinal axis control of an F-16 aircraft. The results suggest that the flexibility provided by an adaptive RHC scheme based on flight condition depen- dent linear prediction models is a necessary requirement for achieving good performance as opposed to a single LTI model based method. The adaptive scheme offers an attractive alter- native to a full nonlinear model based RHC approach by trading off an acceptable degradation in performance to modest com- putational complexity and real-time implementability. 1 Introduction Receding horizon control (RHC) methodologies, also known as model based predictive control methods, have been in the limelight of significant research efforts, motivated by several successful industrial applications [6, 1, 12]. The process in- dustry provided a perfect fit for these algorithms that respected critical process-constraints to achieve safer and more efficient operation of industrial plants. These applications were not only “well-suited” for RHC methods but due to their relatively slow dynamics (large time constants), the significant computational effort of repetitive optimization, which is inherently involved in receding horizon approaches, could be accommodated by the relatively infrequent updates of the control signal. In the past few decades it became apparent that predictive con- trol methods possess qualities that could be utilized in more complex, nonlinear applications, possibly with much faster dy- namics [14]. As more and more of these cutting edge systems (e.g. active suspension [7], gas turbine engine [8], civil aircraft [15], etc.) emerge as applications, for which RHC methods could provide a candidate solution, it is left to the system engi- neer to choose the particular approach from the many flavors of RHC design or possibly a combination of them, which best fits the problem at hand. A main consideration of RHC schemes is real-time implementation, i.e. whether sufficient computational resources are available to accommodate repetitive solution of the optimization problem within each sampling time interval. This paper intends to highlight these issues in the application of three receding horizon control schemes to the longitudinal axis control of a nonlinear F-16 aircraft. The selection of the reced- ing horizon algorithms was motivated by the following aspects of predictive controller design: process modelling, optimiza- tion method and complexity, and real-time implementability. To maintain a common ground for comparison of these meth- ods, specific details of the optimization problem are kept the same for each approach. The results presented in Section 5 de- scribe trade-offs that could be helpful in selecting a particular method for high-end applications. 2 F-16 modelling The nonlinear model of the F-16 aircraft used in simulations and the problem formulation was obtained from [16] and is available at the web-site [17] as a low fidelity model. The dy- namics of the continuous time aircraft model is represented as (1) The mathematical model uses simplified high-fidelity data from NASA Langley wind-tunnel tests conducted on a scale model of an F-16 aircraft [13]. For our investigations, only the longitudinal motion of the aircraft is considered and the states and controls in the model are defined as where stands for altitude [ft], for pitch angle [rad], for total airspeed [ft/s], for angle of attack [rad], for pitch rate [rad/s], for thrust [lb] and for elevator deflection [deg]. Actuators for the control surface and engine are modelled as first-order systems, details of which can be found in [11]. 2.1 Inner-loop control The nonlinear F-16 model in (1) was augmented with an inner- loop controller based on pitch rate feedback. A benefit of the augmented system is stability of the closed-loop vehicle. Output predictions of an unstable system can cause numerical problems in optimization software [12]. This underscores the practical importance of having a stabilizing controller augment the unstable plant before RHC methods are applied (this of course is not a theoretical necessity). Another practical reason for employing an inner-loop in the receding horizon framework is that the RHC sampling rate can be reduced since the inner- loop is handling the high bandwidth disturbance and tracking requirements with its smaller sampling time implementation. This allows more computational time for the outer-loop RHC algorithm (even though the horizon lengths are expected to be longer). Furthermore, actual aircraft often come equipped with an inner-loop flight control system (most commonly stability or control augmentation systems – SAS/CAS). Even in case of an experimental aircraft, which serves as a controller testbed, flight control engineers are very reluctant to implement and test control algorithms without the existing, stabilizing inner-loop control system, which has been flight certified. Therefore, it is reasonable to assume that an inner-loop controller will aug- ment the actual aircraft due to safety, certification or other im- plementation requirements. In this paper, a pitch rate tracking linear -controller was chosen to provide a similar level of performance throughout a