Abstract
This paper presents a control scheme that allows height position regulation and stabilization for an unmanned planar vertical takeoff and landing aircraft system with an inverted pendular load. The proposed controller consists of nested saturations and a generalized proportional integral (GPI). The GPI controls the aircraft height and the roll attitude; the latter is used as the fictitious input control. Next, the system is reduced through linear transformations, expressing it as an integrator chain with a nonlinear perturbation. Finally, the nested saturation function-based controller stabilizes the aircraft’s horizontal position and the pendulum’s angle. Obtaining the control approach was a challenging task due to the underactuated nature of the aircraft, particularly ensuring the pendulum’s upright position. The stability analysis was based on the second method of Lyapunov using a simple candidate function. The numerical simulation confirmed the control strategy’s effectiveness and performance. Additionally, the numerical simulation included a comparison against a PD controller, where its corresponding performance indexes were estimated, revealing that our controller had a better response in the presence of unknown disturbances.
Highlights
Mathematical Problems in Engineering and landing (PVTOL) aircraft, a simplified model of the actual vertical takeoff and landing aircraft [9], which encompasses almost all the dynamics found in real unmanned aerial vehicle (UAV). e PVTOL has been used as a suitable benchmark to test new and existing controllers because it behaves like the well-known quadrotor in a two-dimensional plane. ere exist many works that tackle the PVTOL stabilization problem
Hehn et al [16] proposed this problem in 2011 and named it the flying inverted pendulum, consisting of an inverted pendulum attached to a quadcopter. e control goals of this study are stabilization at the origin and tracking a circular trajectory for the quadcopter, using linear quadratic regulator (LQR) control in both cases. e fact that the pendulum weights less than 5% of the UAV weight allows us to separate its corresponding dynamics
We propose a control scheme for a PVTOL aircraft system with an inverted pendular load (PVTOL-ASIPL). is scheme mainly consists of a generalized proportional integral (GPI) controller and a nested saturation-based control. e GPI controller accomplishes height and roll attitude control, using the roll attitude angle as fictitious input control. en, proposing a set of convenient linear transformations and reducing the system can be expressed as a chain of integrators with a nonlinear perturbation
Summary
Mathematical Problems in Engineering and landing (PVTOL) aircraft, a simplified model of the actual vertical takeoff and landing aircraft [9], which encompasses almost all the dynamics found in real UAVs. e PVTOL has been used as a suitable benchmark to test new and existing controllers because it behaves like the well-known quadrotor in a two-dimensional plane. ere exist many works that tackle the PVTOL stabilization problem. Once the GPI law stabilized the PVTOL aircraft height, a change of coordinates allows expressing the system as a chain of integrators nonlinearly perturbed, allowing to propose the nested saturation function-based stabilizing controller. After α ⟶ αd and applying the controller u2, the following system of equations represents the PVTOL aircraft system with an inverted pendular load: x€v ex1 + ex2 , 2mvmv + mp
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