Mathematical Problems in Engineering

Volume 2015 (2015), Article ID 254975, 15 pages

http://dx.doi.org/10.1155/2015/254975

## Flight Envelope Protection Control Based on Reference Governor Method in High Angle of Attack Maneuver

^{1}Jiangsu Key Laboratory of Internet of Things and Control Technologies, Nanjing University of Aeronautics and Astronautics, Nanjing, Jiangsu 210016, China^{2}College of Automation Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, Jiangsu 210016, China

Received 14 September 2014; Revised 17 January 2015; Accepted 21 January 2015

Academic Editor: Giuseppe Rega

Copyright © 2015 Hui Ye et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The reference governor strategy is presented for the flight envelope protection control of the aircraft during high angle of attack maneuvers. Limits of key flight parameters and amplitude saturation of control surfaces are explicitly considered by imposing the output and input constraints on the flight system. Firstly, a nominal flight control scheme is designed using eigenstructure assignment approach. The static and dynamic reference governors are discussed for flight envelope protection control of the aircraft during stability-axis roll maneuver. Then, a new reference governor is presented based on step response model. The performance of these reference governors for flight envelope protection is demonstrated and compared by numerical simulations. Results show that the dynamic reference governor and the proposed step response model based reference governor are valid for the flight envelope protection control and the latter is easier to be realized.

#### 1. Introduction

The control problem for systems with input and output constraints has substantially attracted researchers’ attention during the past decades. Various control strategies have been proposed to solve this problem (see [1]). Among these existing strategies, antiwindup is an effective approach to deal with systems with input constraints [2, 3], and override can be used to handle output constraints. In addition to this method, there exist other effective techniques to deal with systems with input constraints and output constraints, for example, model predictive control [4, 5] or reference governor [6–14].

The reference governor, also called command governor and reference management device, is a practical method to deal with the constrained tracking control problem. It is a nonlinear device which is located between the original reference command and the input to the closed-loop system. The reference governor can modify the original reference in an appropriate way and a virtual command is produced for the closed-loop system to avoid violation of input and output constraints. To establish the inner closed-loop system, a nominal controller should be designed. And the output of the reference governor is employed as the input of the inner closed-loop system. The advantage of this scheme is that the reference governor does not change the performance of inner closed-loop system which is ensured by the nominal controller when the system is far away from its constraints. This is a grateful property for many practical applications which have requirements on both tracking performance and constraint fulfillment.

In the engineering practice, the low-pass filter can be considered as the basic type of the reference governor with open-loop form. However, this form is quite conservative. A more effective method is the closed-loop reference governor which can modify the reference based on the current system state. Up to now, several reference governors of this form have been developed. Gilbert et al. [6] studied two discrete-time reference governors including the static and the dynamic forms for linear control systems with state and control constraints. These methodologies were improved in [7], in which the disturbance inputs were considered. A reference governor is proposed based on conceptual tools of predictive control for constrained linear time-invariant systems by Bemporad et al. [8]. In [9], it was extended to the time-variant case and obtained a robust command governor. This type of reference governor was applied to an inverted pendulum in [10]. Kogiso and Hirata [11] constructed a reference governor in the form of a piecewise affine function of the state. Reference governors for constrained nonlinear systems have been also studied [12–14]. However, when these methods are implemented in the practice of the flight envelope protection control, the admissible sets of the system used in the reference governors are complex and difficult to be obtained.

The flight envelope protection control of the aircraft in high angle of attack maneuver can be treated as a constrained control problem for which the reference governor is available. The safe flight regime is commonly described in terms of constraints on key parameters, airspeed and angle of attack. Other limitations related to the flight state of the aircraft may come from the saturation of control surfaces. The task of the flight envelope protection control is to track the commands from the cockpit. At the same time, the aircraft should stay within the boundaries of the envelope. The traditional limiter scheme is inefficient when the aircraft maneuvers at high angle of attack. Pilots need to monitor cockpit instruments when operating the aircraft to execute the desired maneuvers. Advanced flight envelope protection control system could reduce pilot’s workload and improve the safety of the aircraft. Although lots of control laws have been developed for the aircraft to perform maneuvers at high angle of attack well [15, 16], few of them take the envelope protection problem into consideration. van Oort et al. [17] developed a controller for F-16/MATV aircraft model to maneuver at high angle of attack combined with a stability-axis roll by a combination of feedback linearization and robust model predictive control (MPC). The constraints on the input and state were transformed to linear matrix inequality (LMI) constraints of the optimization problem of the MPC. In [18], an antiwindup compensator was designed for the aircraft model with input saturation. However, the constraints on outputs were not considered. Falkena et al. [19] investigated the effect of four approaches for the flight envelope protection: control limiting, command limiting, constrained flight control law, and virtual control limiting. The results indicated that for practical implementation command limit is the best choice. But only hard limits were imposed on the commands and the dynamic of the closed-loop system was not considered. In this paper, the reference governor is employed to adjust the original reference based on the current state which contains the dynamic information of the system and guarantees that the system satisfies its input and output constraints during transient or steady.

The principle of the reference governor has similarities with model predictive control [10, 14]. In absence of information on the future evolution of the reference, two reasonable assumptions can be used to make a prediction: the impulse signal assumption and the step signal assumption. In [6], the static reference governor is based on the impulse signal assumption and other reference governors are based on the step signal assumption. By invoking the latter, it is more convenient to use the increment of the reference signal than the signal itself. Thus, the step response model used in dynamic matrix control (DMC) is more favorable for the design of the reference governor in the practice of flight envelope protection control. Motived by above analysis, the reference governor strategy is presented for the flight envelope protection control of aircraft during the high angle of attack maneuver based on the step signal assumption.

The paper is organized as follows. Section 2 formulates the control problem and basic scheme of the reference governor strategy. Section 3 describes the static and dynamic reference governors proposed by [6], which is designed using the concept of the maximal admissible set. By using the step response model in DMC, a novel reference governor is proposed in Section 4. A constrained aircraft model is introduced in Section 5. Before the reference governor is applied to the flight envelope protection, a nominal flight controller is designed to meet the flying quality requirements using eigenstructure assignment approach. In Section 6, the studied three reference governors are applied to the flight envelope protection of the aircraft in high angle of attack maneuver. The maximal admissible set of the static and dynamic reference governor is calculated while the initial admissible set used in the step response model based reference governor is also given. Simulation results of each reference governor are presented. The advantages and disadvantages of them are discussed. Finally, Section 7 includes some conclusions.

The following notations will be used in this paper. is the set of nonnegative integers. is the notation for set of real vectors. The superscript denotes vector or matrix transpose. The vectors and matrixes used in this paper are notated in boldface and the subsets are notated in decorated letter. is the image of under . and denote the th row of the matrix and the vector , respectively.

#### 2. Problem Formulation and Reference Governor Strategy

In order to implement the reference governor into the system, the following discrete-time linear time-invariant equation with input and output constraints is considered: where is the state vector and is the input vector which has amplitude saturation constraints; is the output which is required to track the commands; is the output on which constraints are imposed; are matrices with corresponding dimensions. The input and output constraints can be described as , ; and are convex and compact sets and are usually expressed as the following form:

The reference governor control strategy consists of a nominal controller and a reference command governor, as depicted in Figure 1. The nominal controller is equipped for obtaining good linear-system properties, that is, the satisfactory tracking performance of . It is designed via classic linear control methods. Here, a full state feedback control law is given as follows: where is the feedback gain matrix to make system asymptotically stable and is the reference input matrix to eliminate the error between and , satisfying The virtual command is the output of reference governor, which can be considered as a compromise of the original reference . The task of reference governor is to modify the original reference to avoid constraints violation of input and output and to ensure that the output virtual command is a good approximation of the original reference. The reference governor of closed-loop form can be considered as a prefilter with its parameters varying by the current state and reference.