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کد پروژه: 156781


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Virtual-command-based model reference adaptive control for abrupt structurally damaged aircraft

a b s t r a c t

Although a high-gain learning rate can offer ideal tracking performance in adaptive control in theory, it can also lead to high-frequency oscillations in practice due to the unmodeled dynamics of the system. In aircraft structural damage scenarios, the strong uncertainty and the safety-critical nature of the problem make this conflict critical. In this paper, a novel virtual-command-based model reference adaptive control (MRAC) scheme for flight control is proposed. 

1. Introduction Structural damage to the airframe of a modern aircraft, such as structural failure in the wing tip, vertical tail or engine, is one of the most serious threats that pilots face. Such structural damage may lead to significant, abrupt and non-symmetric uncertainties in the aircraft aerodynamics, mass properties, and control efficiencies [1,2]

A classic approach is to modify the reference model [16,11,17, 18]. A closed-loop reference model (CRM) structure was proposed in [16,11], in which plant information was used to alter the reference trajectory to improve the transient properties. [17] introduced a new reference system to prevent the update law from attempting to learn from high-frequency system error content. Because the CRM approach does not introduce new information to the controller, i.e., the learning process is still driven by the tracking erro

he learning error is more efficient. The remainder of this paper is organized as follows. Section 2 introduces the model of a damaged aircraft. Section 3 presents a standard linear-parameter-varying-model-based model reference adaptive control scheme (LPV-MRAC). Section 4 analyzes the transient performance of LPV-MRAC. A new approach, called virtualcommand-based MRAC (VC-MRAC), is proposed in Section 5 to improve the transient performance. A simulation of the generic transport model (GTM) in a scenario in which the left wing tip has broken off is discussed in Section 6. Finally, conclusions are given in Section 7.

2. Plant models and problem formulation In this paper, a linear parameter-varying (LPV) model is used to represent the dynamics of a structurally damaged aircraft as follows: x˙ = A(λ)x + B(λ)u + Dd(λ),

3. LPV-MRAC scheme In this section, an LPV-MRAC controller is presented based on the standard MRAC design procedure. In particular, a virtual command v is introduced as the input to the LPV-MRAC controller instead of the actual input r. Correspondingly, er x − xmr and ev x − xmv are defined as the actual and virtual tracking

4. Transient performance of LPV-MRAC While the above LPV-MRAC method has been proven to be Lyapunov stable, the virtual tracking error is not guaranteed to be asymptotically stable and may be very large during the transient period, i.e., the learning period of the adaptive control system. In practice, a large transient tracking error may drive the aircraft into a nonlinear or unmodeled region, resulting in failure of the adaptive control law. Therefore, the tracking error must be bounded in a safe range

5. VC-MRAC scheme In this section, a virtual-command-based scheme is introduced to improve the transient tracking performance while maintaining the robustness of the MRAC scheme. The transient dynamics with respect to v can be approximated by reformulating Eq. (13) as follows:

6. Application to the generic transport model 6.1. The GTM and the control objective To illustrate the proposed adaptive control scheme, we conducted simulations of the GTM with the left wing tip broken, as shown in Fig. 1. The nonlinear aerodynamic coefficients of aircraft with left wing-tip damage (0 to 33% semi-span) are provided in Ref. [35]. The dynamics of such an aircraft are described by the following general nonlinear ordinary differential equation: X˙ = f (X, u,λ), (39)

The uncertainties and disturbances are as follows: 1) The system dynamics vary with damage, as reported in Ref. [35], and the approximate polytopic model presented in the following subsection describes the variation of the system matrix. 2) The control efficiency uncertainty induced by the damage is (t) = diag([0.6, 0.8, 0.7])(t > td).

6.2. LPV-MRAC performance evaluation An LPV-MRAC scheme was designed for the operating point of v = 45.3 m/s, α¯ = 4.096 deg, H = 304.8 m and u = [1.77, 0, 0] deg. By means of a higher-order singular value decomposition procedure [33], the attitude dynamics with broken-off wing-tip damage ranging from 0 to 33% of the semi-span can be approximated by an LPV model with 3 vertices as follows:

7. Conclusion To achieve high transient performance in the event of abrupt and severe structural damage to an aircraft, a virtual-commandbased model reference adaptive control (VC-MRAC) scheme was proposed. In comparison with the classic approach, a virtual command and a virtual tracking error were introduced to break the direct relationship between the learning law and the actual tracking error. The design process for the virtual command controller and the learning error observer were further studied in detail. A system-theoretical analysis and illustrative numerical examples were presented to demonstrate that the new approach is effective in maintaining high tracking performance with improved robustness compared with the standard MRAC scheme. Future research will include studies on the application of the proposed scheme in combination with other adaptive control approaches and in nonlinear systems

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