A New Nonlinear Controller for Trajectory Tracking of the Longitudinal Dynamics of a Small Scale Helicopter

A nonlinear control scheme is proposed for the trajectory tracking problem of a small scale helicopter’s longitudinal dynamics. The control scheme is based on a control design procedure that constructs static feedback regulators for nonlinear systems which are linearizable by dynamic feedback. Besides, the flatness characteristics of the helicopter’s longitudinal dynamics are used to design the desired trajectory. The controller proposed is based on the longitudinal model of the small scale helicopter including the main rotor and stabilizer bar dynamics. Sufficient conditions are given to guarantee asymptotic convergence to zero of the tracking error and to keep the main rotor thrust always negative assuming that all the helicopter’s parameters are known and that all helicopter’s states are measured. Numerical simulations are given to show the performance of the controller in the presence of the main rotor and stabilizer bar dynamics.     

Structure invariance for uncertain nonlinear systems

A unified study of three control problems associated to multi-input multi-output nonlinear systems with uncertainties is presented, namely, input-state linearization by static state feedback, input-output decoupling by static state feedback and input-output decoupling by dynamic compensation. For each of these problems, geometric conditions which describe intrinsic structural invariance properties are given     

Sliding Mode Control and State Estimation for a Class of Nonlinear Singularly Perturbed Systems

This paper is concerned with the design of a controller-observer scheme for the exponential stabilization of a class of singularly perturbed nonlinear systems. The controller design uses a sliding mode technique and is divided in two phases: slow feedback control and fast feedback control so that a final composite control is obtained. Assuming that only the fast state is available and the system's output is a function of the slow state, an observer design is presented. A stability analysis is also made to provide sufficient conditions for the ultimate boundedness of the full order closed-loop system when the slow state is estimated by means of the observer. An application to the model of a permanent magnet stepper motor is given to show the controller-observer methodology and stability analysis.     

The disturbance decoupling problem for time-delay nonlinear systems

In this paper, the disturbance decoupling problem (DDP) for a class of SISO nonlinear systems with multiple delays in the input and the state is studied. A pioneering mathematical approach is introduced for this class of systems and is claimed to be the cornerstone of the problem. Necessary and sufficient conditions are given for the existence of a bicausal feedback that solves the DDP. Sufficient conditions for the existence of a solution within other classes of compensators are included as well     

Adaptive Passivity of Nonlinear Systems Using Time-Varying Gains

In this paper, an adaptive controller with time-varying gains is proposed to solve the problem of making a single-input single-output (SISO) nonlinear system, with explicit linear parametric uncertainty, equivalent to a passive system. Some stability issues associated to the resultant closed-loop passive system are also discussed. The results obtained are applied to two examples, a third order nonlinear system and a model of a magnetic levitation system, to show the controller methodology design.     

On robust regulation via sliding mode for nonlinear systems

A robust control scheme for the output tracking of nonlinear systems is proposed. The scheme is based on the nonlinear regulator theory and the sliding mode approach. It is shown that if perturbations and/or uncertainties appear on the system, the sliding mode controller is able to perform approximate asymptotic tracking, in the sense that the output tracking error remains bounded, provided the upper bounds of the uncertain terms are known.     

Sliding Mode Rest-to-Rest Stabilization and Trajectory Tracking for a Discretized Flexible Joint Manipulator

In this article, a difference flatness approach is used for trajectory tracking tasks of an approximately (Euler) discretized model of a nonlinear, single link, flexible joint manipulator. The system's flat output is commanded to follow a prescribed trajectory achieving a desired angular position maneuver. A new robust discrete time feedback controller design technique, of the sliding mode type, is then proposed for the closed loop regulation of the link position around the prescribed trajectory. The effectiveness of the approach is illustrated by means of digital computer simulations in a rest-to-rest stabilization maneuver and in a sinusoidal reference trajectory tracking task.     

Direct passivity of a class of MIMO non-linear systems using adaptive feedback

In this paper, an adaptive controller with adaptive laws specially designed is proposed to solve the problem of making a multi-input multi-output (MIMO) non-linear system, with explicit linear parametric uncertainty, equivalent to a passive system. These results are an extension of those obtained by the authors for the SISO case. Some stability issues associated to the resultant closed-loop passive system are also discussed. The results obtained are applied to models of dynamical MIMO systems, to illustrate the controller design methodology.     

Control of a flexible joint robot manipulator via a non-linear control-observer scheme

A non-linear controller-observer scheme for the output tracking of a class of non-linear singularly perturbed systems based on a two-time scale sliding-mode technique and a high gain estimator, is presented. An analysis of stability of the resultant closed-loop system is given. The proposed scheme is applied to the model of a two degrees of freedom flexible joint robot to show the controller-observer methodology proposed.