Research articleA neural network based MRAC scheme with application to an autonomous nonlinear rotorcraft in the presence of input saturation☆
Introduction
Rotorcraft has demonstrated its gift at vertical taking off and landing capability, precise stationary hover flight, rapid motion ability, and superior agility [1]. With the ability to reach complex and confined environments, rotorcraft is capable of conducting missions that is not feasible for normal fixed-wing aircraft. Complex aerodynamic characteristics between rotor and airframe requires controllers with stronger robustness and better decoupling ability compared with fixed-wing aircraft. Over the past several years, adaptive control system design of autonomous rotorcraft attracts researchers’ attention.
As an important approach of adaptive control, model reference adaptive control (MRAC) reveals not only its ability of ensuring closed-loop system stability and tracking performance despite parameter uncertainty but also compatibility of various control techniques (e.g. input saturation [2], neural network [3]) to achieve different control objectives. Development of MRAC control theory has tended to be mature after decades of research [4], [5], refinements and improvements of MRAC control scheme for many practical applications, such as flight control systems, especially the rotorcraft flight control systems, are still needed.
Although advanced flight control has been studied for rotorcraft control system design, simplified rotorcraft models were used to design and test adaptive flight control laws. It should be noted that higher order dynamics of rotorcraft such as blade flapping motions and engine dynamics has significant impact on stability and performance of rotorcraft flight control laws [6], [7]. In extreme operation environment (e.g. shipboard operation), either the gust or the airwake has tremendous influence on rotor dynamics and subsequently affects the whole helicopter [8]. One can design a controller ignoring rotor dynamics, but the flight quality degrade and loss of stability usually occurs because the rotor dynamics was not taken into consideration in controller design. To avoid such problems, a helicopter model with blade flapping dynamics and engine dynamics is presented in this paper.
As discussed previously, controllers with high robustness and strong decoupling ability against nonlinearity and coupling in the design of rotorcraft control law are required. Neural network adaptive control emerges because of the good capability of approximating and compensating unknown uncertainty and nonlinearity related to system states and inputs. A neural-network-based adaptive controller was designed to achieve load factor and rotor stall limit protection for GTMax rotorcraft in [9]. The trajectory tracking problem was investigated for a model-scaled helicopter using adaptive neural network control approach in [10]. As a kind of neural network method, RBFNN is appropriate for the control law design due to the ability of faster convergence and local approximation which avoids the local minimum problem. With such ability, neural network is also widely applied on fault diagnosis and fault tolerant control [11], [12], [13], [14]. Unlike fault detection and diagnosis of high-speed railway developed in [13], [14], proposed neural-network-based MRAC scheme is able to track reference signals without fault estimation by regarding minor fault as part of system uncertainty. Furthermore, input saturation problem has been considered in the design of flight control laws (e.g. hypersonic vehicle [15], missile [16], surface vessel [17]). Combined with back-stepping control method, hyperbolic tangent functions were used to deal with input saturation problems, while these functions are rarely used in rotorcraft control problem under MRAC structure.
One major contribution of this article is that a RBFNN-based MRAC scheme is proposed for the multi-input multi-output (MIMO) rotorcraft in the presence of input saturation. Through hyperbolic tangent functions, control saturation will not occur owing to the modified reference model under MRAC structure. RBFNN used in the design of adaptive law guarantees the rapid approximation of control gains. Moreover, stability of the closed-loop rotorcraft system is demonstrated and analyzed in detail in this paper.
Another contribution is that the proposed MRAC scheme, designed with combination of performance specification handling qualities requirements from ADS-33E [18], is applied to a nonlinear rotorcraft model to verify the effectiveness through Mission-Task-Elements (MTEs). In this paper, the MRAC scheme is developed based on linearization of the nonlinear rotorcraft and then applied to the nonlinear rotorcraft model. However, modeling error/uncertainty between linear and nonlinear model could lead to some residual errors even parameter drift under such a method, which brings the demand of robust modifications of the adaptive controller design, such as -modification [19] and projection operator [20]. To prevent systems from parameter drift using such linearization-based method, a modified projection operator is proposed combined with RBFNN adaptive control technique in this paper. Effectiveness of proposed control scheme is demonstrated through simulations.
The rest of this paper is organized as follows. Section 2 formulates the nonlinear and linearized model of rotorcraft for control scheme design. A RBFNN-based nonlinear MRAC scheme under input saturation is proposed in Section 3 and applied to the nonlinear rotorcraft model. Simulation results and analysis are provided in Section 4 for the autonomous rotorcraft in various flight missions combined with specifications in ADS-33E. Section 5 draws the conclusions.
Section snippets
Dynamic of mathematical rotorcraft model
In this section, a nonlinear mathematical rotorcraft model with blade flapping dynamics and engine dynamics is developed. This model is composed of dynamics of rigid-body and dynamics of rotor motions, which includes main rotor, tail rotor, empennage and fuselage. Details of this model can be found in [21], [22]. The nonlinear model is given by in which where represent translational
Nonlinear MRAC scheme with input saturation
Model reference adaptive control is widely adopted in advanced control systems design of rotorcraft. The MRAC-based controller adjusts the feedback and feedforward gains automatically according to the change of rotorcraft states through multiple flight regimes. Therefore, the MRAC scheme is applicable in a wide range of flight conditions. In this section, a saturated nonlinear MRAC scheme is conducted and applied to a nonlinear rotorcraft.
Simulation study
In this section, the nonlinear MRAC scheme proposed in Section 3 is applied to the nonlinear rotorcraft model with the consideration of handling qualities specifications according to ADS-33E.
Conclusions
In this paper, a multivariable MRAC scheme is proposed in the presence of input saturation and has been demonstrated the effectiveness with application to a nonlinear rotorcraft. Hyperbolic tangent functions are utilized to handle input saturation under MRAC structure. MRAC laws designed with RBFNN and modified projection operator ensure the fast and accurate tracking of the command signals and prevent the nonlinear rotorcraft from parameter drift. In addition, the MRAC scheme is developed to
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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This work was supported by the Aviation Science Foundation of China under Grants 20180753005.