Adaptive stable control of manipulator system based on immersion and invariance

This work focused on the manipulator system containing uncertainties, and proposes an immersion and invariance (I&I) control strategy, in order to avoid the damage on the mechanical and the operation object caused by parameter uncertainty. A stable target system with lower dimension than the manipulator system was chosen to design the control law and estimation laws of uncertain parameters. Then finding an invariant and attractive manifold in state space with internal dynamics a copy of the desired closed-loop dynamics. Finally, design a control law that can steer the state of the system sufficiently close to the manifold. The immersion and invariance adaptive control does not rely on certainty equivalence. The whole uncertain parameter estimations are the sum of two terms. One is obtained by an iterative law like the traditional adaptive backstepping method. On the other hand, a nonlinear function is introduced. The role of this additional term makes the parameter estimations more exible and effective. Lyapunov function is not necessary for the process of designing adaptive controllers. So immersion and invariance can effectively avoid the 'computing expansion' of backstepping method. Compared with the traditional adaptive methods, simulation results show that the proposed immersion and invariance adaptive controller can improve the system performance, including dynamic response, stability and accuracy of parameter estimations

Sliding mode control of a class of underactuated system with non-integrable momentum

In this paper, a sliding mode control scheme is developed to stabilise a class of nonlinear perturbed underactuated system with a non-integral momentum. In this scheme, by initially maintaining a subset of actuated variables on sliding manifolds, the underactuated system with the non-integrable momentum can be approximated by one with the integrable momentum in finite time. During sliding, a subset of the actuated variables converge to zero and a physically meaningful diffeomorphism is systematically calculated to transform the reduced order sliding motion into one in a strict feedback normal form in which the control signals are decoupled from the underactuated subsystem. Furthermore, based on the perturbed strict feedback form, it is possible to find a sliding mode control law to ensure the asymptotic stability of the remaining actuated and unactuated variables. The design efficacy is verified via a multi-link planar robot case study

Robust finite-time position and attitude tracking of a quadrotor UAV using super-twisting control algorithm with linear correction terms

This work investigates the problem of finite-time position and attitude trajectory of quadrotor unmanned aerial vehicle systems based on a modified second order sliding mode algorithm. The selected algorithm is a modified super-twisting with both nonlinear and linear correction terms.CONACYT – Consejo Nacional de Ciencia y TecnologíaPROCIENCI

A new solution to the problem of range identification in perspective vision systems

Published versio

Adaptive, Neural and Robust Control of Wing-Rock and Aeroelastic System

Modern aircraft exhibit wing-rock phenomenon and aeroelastic instability. Wingrock (roll single degree of freedom motion) and aeroelastic systems\u27 (two degrees of freedom) behavior are described by complex nonlinear differential equations. The nonlinearities in the dynamics of these systems give rise to limit cycle oscillations beyond critical speed of aircraft. The onset of wing-rock and aeroelastic instability limits the performance of aircraft and can even lead to catastrophic consequences. Therefore, control of wing-rock motion and stabilization of aeroelastic systems are important. In the past, several studies have been made and experimental and analytical results have been obtained to explain the wing-rock and aeroelastic phenomena in wind-tunnel tests, and also control systems have been derived. Motivation for this research is the importance of flying aircraft in a large flight envelope in which complex uncertain aerodynamic nonlinearities appear, causing instabilities and flutter in the aircraft wings. For the control of wing-rock motion and the stabilization of aeroelastic instabilities, new control systems are designed. Because modeling of nonlinear dynamics of wing-rock motion and aeroelastic systems are imprecise, the control algorithms must be insensitive to model uncertainties. Apparently control theory for deterministic systems is not applicable to uncertain systems. For the stabilization of wing-rock, two non-certainity equivalent adaptive (NCEA) laws are designed. The first control system includes a finite form realization of a speed-gradient adaptation law, and the second controller is based on the Immersion and Invariance (I&I) theory. For the nonlinear multi-input multi-output (MIMO) aeroelastic systems, equipped with leading- and trailing-edge control surfaces, four distinct control systems are designed. First, a Chebyshev neural adaptive control law is derived for the suppression of limit cycle oscillations (LCOs) of the prototypical wing. For this derivation SDU decomposition of the high-frequency constant gain matrix is utilized for obtaining a singularity free controller. Then for a multi-input aeroelastic system with state dependent input matrix, a higher-order robust sliding mode control law for finite-time stabilization is derived. This is followed by the design of a suboptimal controller based on the state-dependent Riccati equation (SDRE) method. Finally, a suboptimal control law is designed for the control of the aerolelastic system, based dierential game theory. In this approach, the wind gust is treated as an adversary which tries to destabilize system. These control algorithms are simulated using MATLAB and SIMULINK to verify their performance. Results show that the designed controllers are effective in suppressing the limit cycle oscillations

A Linear Active Disturbance Rejection Control for a Ball and Rigid Triangle System

This paper proposes an application of linear flatness control along with active disturbance rejection control (ADRC) for the local stabilization and trajectory tracking problems in the underactuated ball and rigid triangle system. To this end, an observer-based linear controller of the ADRC type is designed based on the flat tangent linearization of the system around its corresponding unstable equilibrium rest position. It was accomplished through two decoupled linear extended observers and a single linear output feedback controller, with disturbance cancelation features. The controller guarantees locally exponentially asymptotic stability for the stabilization problem and practical local stability in the solution of the tracking error. An advantage of combining the flatness and the ADRC methods is that it possible to perform online estimates and cancels the undesirable effects of the higher-order nonlinearities discarded by the linearization approximation. Simulation indicates that the proposed controller behaves remarkably well, having an acceptable domain of attraction