Application of Higher Order Derivatives to Helicopter Model Control

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Control of a helicopter model is a problem of both theoretical and practical interest. With the proliferation of autonomous unmanned aerial vehicles (UAVs) (Castillo et al., 2005; Valavanis, 2007) autopilot modes have become very important. Dynamic properties of a controlled helicopter depend on both its structure and aerodynamic qualities as well as on the control law applied. The problem of output regulation has received much attention and especially during the last decade, its nonlinear version has been intensively developed (Isidori & Byrnes, 1990), (Slotine & Li, 1991). The well known approach to decoupling problem solution based on the Non-linear Inverse Dynamics (NID) method (Balas et al., 1995) may be used if the parameters of the plant model and external disturbances are exactly known. Usually, incomplete information about systems in real practical tasks takes place. In this case adaptive control methods (Astrom & Wittenmark, 1994) or control systems with sliding mode (Utkin, 1992) may be used for solving this control problem. A crucial feature of the sliding mode techniques is that in the sliding phase the motion of the system is insensitive to parameter variation and disturbances in the system. A way of the algorithmic solution of this problem under condition of incomplete information about varying parameters of the plant and unknown external disturbances is the application of the Localization Method (LM) (Vostrikov & Yurkevich, 1993), which allows to provide the desired transients for nonlinear time-varying systems. A development of LM is applied in the present paper, and proposed in (Blachuta et al., 1999; Czyba & Blachuta, 2003; Yurkevich, 2004), method which based on two ideas. The first – the use of high gain in feedback to suppress the disturbances and varying parameters; the second – the use of higher order output derivatives in the feedback loop. The high gain and ”dynamics” of the controller are separated by means of the summing junction with set point signal placed between them. This structure is the implementation of the model reference control with the reference model transfer function which is equal to the inverse of the controller ”dynamics”. It becomes that the proposed structure and method is insensitive to plant parameters changes and external disturbances, and works well both lineal, nonlinear, stationary and nonstationary objects. In the present paper, the proposed method is applied to control of the helicopter model, which is treated as a multivariable system. 10

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