Switching LPV control design with MDADT and its application to a morphing aircraft
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SWITCHING LPV CONTROL DESIGN WITH MDADT
- AND ITS APPLICATION TO A MORPHING AIRCRAFT Yong He, Chunjuan Li, Weiguo Zhang, Jingping Shi and Yongxi Lü.
- In flight control of a morphing aircraft, the design objective and the dynamics may be different in its various configurations.
- It has been recognized that the property in the ADT switching is still not anticipated, since the average time interval between any two consecutive switching is at least τa, which is independent of the system mode.
- So far there is no result available yet on control of switching LPV systems with MDADT based on parameter-dependent Lyapunov functions, which will reduce the conservatism, enhance flexibility and improve the disturbance attenuation performance in the analysis and synthesis of a switched LPV system.
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Frequently Asked Questions (15)
Q2. Why is the morphing aircraft a complicated system?
Due to the significant wing reconfiguration, aerodynamic parameters, which are varied dramatically, will make the morphing aircraft be a complicated system with strong nonlinearity and uncertainties.
Q3. What is the main contribution of this paper?
The main contribution of this paper is that a novel notion of parameter-dependent MDADT switching scheme and a group of parameter-dependent Lyapunov functions are used to investigate the problem of control of switching LPV systems, and then the proposed result is applied to a switching LPV representation of the morphing aircraft to accommodate multiple control objectives in different sweep wing configurations.
Q4. What is the state dimension of each controller?
Each controller, also a function of the parameter ρ, stabilizes the open-loop system with best achievable performance in a specific parameter region, and meanwhile maintains the closed-loop system stability under the given switching strategy.
Q5. What is the simplest way to control an LPV?
for an LPV system with a large parameter variation range, a single Lyapunov function, quadratic or parameter-dependent, may not exist, even if it does exist, it is often necessary to sacrifice the performance in some parameter subregions in order to obtain a single LPV controller over the entire parameter region.
Q6. What is the parameter value measurable in real-time?
It is assumed that ρ is in a compact set P ⊂ Rs with its parameter variation rate bounded by vk ≤ ρ̇k ≤ vk, for k = 1, 2, . . . , s, and the parameter value is measurable in real-time.
Q7. What is the weighting function for the morphing aircraft?
The related weighting functions and are given asWa = diag(0.1, 0.2), Wact = −20 201 0 −20 20 , the other common weighting functions are chosen asWn = diag(0.6, 0.1), Wideal = αideal αcmd = 144 s2 + 19.2s+ 144 ,where the ideal model is a second-order system with the natural frequency 12 rad/s and the damp ratio 0.8.
Q8. What is the input of the open-loop system?
The inputs of the open-loop system include the 2-dimensional sensor noise signal n, the angle of attack command αcmd and the control input u.
Q9. Why is the average dwell time in the morphing aircraft different?
It is by this cause the authors can deliberately adjust the average dwell time in each subregion, i. e. MDADT.5. CONCLUSIONSDue to the large variation of the parameters and multiple control objectives in different configurations for a morphing aircraft, a switched LPV model was obtained and different performance weighting functions were selected to reflect design requirements in its different configurations.
Q10. What is the tracking error in the steady state?
Noting that the tracking error in the steady state is 1.25%, 1.11% and 1%, and the bandwidth in the region 1 is the biggest, meanwhile, in region 3 the bandwidth is the smallest, this is consistent with the design objective.
Q11. What is the simplest way to regulate the air-fuel ratio of an LPV?
In Ref. [14], a switching LPV controller is used to regulate the air-fuel ratio of an internal combustion engine, and all of them have improved system performance in certain extent.
Q12. What is the difference between the sweep and the dashed line?
Whereas the dashed line has different variationrate in different region in order to maintain different dwell time in its subregion, as the dwell time is mode-dependent, the switching signal, which is determined by the sweep signal, is mode-dependent.
Q13. How to develop an LPV representation of the morphing aircraft?
To develop an LPV representation of the morphing aircraft, it is needed to find the wingslevel equilibrium points at several configurations first.
Q14. What is the flight condition of interest?
The flight condition of interest is selected as the altitude H = 1000m, velocity V = 25 m/s, and other parameters in different configurations as listed in Table 1.
Q15. What is the difference between Definition 2.1 and the ADT property?
As can be seen, Definition 2.1 constructs a different set of switching signals from that with the ADT property [7], that is, if there exist positive numbers τap, p ∈ S, such that a switching signal has the MDADT property, it only requires that the average time among the intervals associated with the pth subsystem is larger than τap.