Backstepping with bounded feedbacks

A nonlinear control is proposed for trajectory track-ing of a 6-DOF model-scaled helicopter with constraints on main rotor thrust and fuselage attitude. In the procedure of con-trol design, the mathematical model of helicopter is simplified into three subsystems: altitude subsystem, longitudinal-lateral subsystem and attitude subsystem. The proposed control is developed by combining the sub-controls for the correspond-ing subsystems. The sub-controls for altitude subsystem and longitudinal-lateral subsystem are designed with hyperbolic tangent functions to satisfy the constraints; the sub-control for attitude subsystem is based on backstepping technique such that fuselage attitude tracks the virtual control for longitudinal-lateral subsystem. It is proved theoretically that tracking errors are ultimately bounded, and control constraints are satisfied. Performances of the proposed controller are demonstrated by simulation results.Key words Nonlinear control, trajectory tracking, helicopter control, saturated control Trajectory tracking control design for a 6-DOF autonomous model-scaled helicopter has becomes an interesting and challenging task in recent years, because of the nonlinearities and couplings in its dynamic model [1−2] . Some representative researches include linear control [3] , approximate feedback linearization [2] , backstepping [4−5] , robust H∞ control [6−7] , composite nonlinear feedback [8] , and model predictive control [9] .Traditionally, nonlinear trajectory tracking controls for helicopters are mainly based on some assumptions: 1) constant rotational rate of rotors, 2) simplified expressions for rotor thrusts in case of low fuselage velocity and acceleration, and 3) negligence of small coupling terms (or small body forces). To support the assumptions, however, some other significant issues require further consideration. The desired main rotor thrust should be subjected to saturation; otherwise, excessively large main rotor thrust would result in large acceleration of the fuselage, and the simplified expressions for rotor thrusts are unreasonable. Besides, large rotor thrust requires large collective pitch, increasing drag forces exerted on the rotor blades and deteriorating the assumption of constant rotational rate. Moreover, attitude of the fuselage should be bounded securely for the reason that aggressive attitude often leads to uncontrollability in case of constraint on rotor thrust.Many early works on saturated control [10−13] presented the fundamental principles and applications. Saturated control for nonlinear systems was then developed and summarized [14−17] . Saturated control strategies were applied to some specific projects, such as 3-DOF VTOL aircraft [18−19] , linear motor system [20] , and inverted pendulum [21] . However, researches on saturated control for trajectory tracking of 6-DOF helicopter were relatively rare. Controllers for helicopters subject to input constraints were often designed partially saturated [4, 22−23] due to nonlinearities and couplings...

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“…In advance, the main rotor thrust and fuselage attitude are proved to satisfy constraints (15) and (16).…”

Section: Calculating the Actual Controlsmentioning

confidence: 99%

Nonlinear Control for a Model-scaled Helicopter with Constraints on Rotor Thrust and Fuselage Attitude

Zhu

Huo

2014

Acta Automatica Sinica

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“…it is zero at zero, strictly increasing and becomes unbounded as its argument increases to infinity [12]. The time derivative of the overall Lyapunov function U yields …”

Section: Control Design and Torque Boundmentioning

confidence: 99%

“…In this work, we design a nonlinear backstepping attitude controller using the inverse tangent based tracking function [4] and a family of augmented Lyapunov functions [12]. Using this control law, we derive an analytical upper bound of the control torque norm.…”

Section: Introductionmentioning

confidence: 99%

Backstepping Control Design with Actuator Torque Bound for Spacecraft Attitude Maneuver

Ali

Radice

Kim

2010

Journal of Guidance, Control, and Dynamics

161

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“…Refs. [15][16][17][18] also addressed this issue. If a nonlinear system is equivalent to a low-triangular form by state feedbacks and coordinate changes, it is possible to design a controller by the backstepping technique.…”

Section: Introductionmentioning

confidence: 99%

Geometric characterization of multi-input lower-triangular forms

Zhang

Tarn²,

et al. 2011

Sci. China Inf. Sci.

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This paper is concerned with the problem as to whether a multi-input nonlinear system is equivalent to the so-called low-triangular form. Two elemental forms of multi-input lower-triangular systems are proposed. Then, using the theory of singular distributions, the necessary and sufficient conditions under which multiinput nonlinear systems are locally feedback equivalent to these two lower-triangular systems are established. Furthermore, algorithms are provided to describe how to realize these equivalent transformations via state feedbacks and coordinate conversions. CitationZhang D, Tarn T J, He X X, et al. Geometric characterization of multi-input lower-triangular forms.

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Backstepping with bounded feedbacks

Abstract: An extension of the backstepping approach is proposed. It allows to globally asymptotically stabilize by bounded feedbacks families of nonlinear control systems. Explicit expressions of control laws and Lyapunov functions are given.

Cited by 59 publications

References 13 publications

Nonlinear Control for a Model-scaled Helicopter with Constraints on Rotor Thrust and Fuselage Attitude

Nonlinear Control for a Model-scaled Helicopter with Constraints on Rotor Thrust and Fuselage Attitude

Backstepping Control Design with Actuator Torque Bound for Spacecraft Attitude Maneuver

Geometric characterization of multi-input lower-triangular forms

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