Output Feedback Controller Design for a Class of MIMO Nonlinear Systems Using High-Order Sliding-Mode Differentiators With Application to a Laboratory 3-D Crane

This paper addresses the problem of output feedback control design for a class of multi-input-multi-output (MIMO) nonlinear systems where the number of inputs is less than that of outputs. There are two difficulties in this design problem: 1) too few control inputs will not generally allow independent control over all outputs and 2) the state of the system is not available for measurements, and only the outputs are available through measurements. To address the first issue, a practical output feedback control problem is formulated, aiming to regulate only part of the outputs, and a controller structure with two design components in all or some chosen control inputs is proposed. To cope with the second difficulty, the recently developed high-order sliding mode differentiators (HOSMDs) are used to estimate the derivatives of the outputs needed in the controller design. With the derivatives estimated using HOSMDs, an output feedback controller is designed using the backstepping approach. Stability results are established for the designed controller under certain conditions. In order to test the applicability of the proposed output feedback controller in practical industrial problems, experiments are carried out though implementing the controller on a laboratory-scale 3-D crane. The experimental results are presented and reveal the advantage of the proposed controller structure, as well as the effect of controller gain and sampling periods

Optimal sliding mode controllers for attitude tracking of spacecraft

This paper studies two optimal sliding mode control laws using integral sliding mode control (ISM) for some spacecraft attitude tracking problems. Integral sliding mode control combining the first order sliding mode and optimal control is applied to quaternion-based spacecraft attitude tracking manoeuvres with external disturbances and an uncertainty inertia matrix. For the optimal control part the state dependent Riccati equation (SDRE) and Control Lyapunov function (CLF) approaches are used to solve the infinite-time nonlinear optimal problem. The second method of Lyapunov is used to show that tracking is achieved globally. An example of multiaxial attitude tracking manoeuvres is presented and simulation results are included to verify the usefulness of these controllers

Robust motion control SMC point of view

In this paper the robust motion control systems in the sliding mode framework are discussed. Due to the fact that a motion control system with n d.o.f may be mathematically formulated in a unique way as a system composed of n second order systems, design of such a system may be formulated in a unique way as a requirement that the generalized coordinates must satisfy certain algebraic constraint. Such a formulation leads naturally to sliding mode framework to be applied. In this approach constraint manifolds are selected to coincide with desired constraints on the generalized coordinates. It has been shown that the CMC can be interpreted as a realization of the acceleration controller thus possessing all robust properties of the acceleration controller framework. The possibility to treat both unconstrained motion (the motion without contact with environment) and constrained motion in the same way is shown

Sliding-mode neuro-controller for uncertain systems

In this paper, a method that allows for the merger of the good features of sliding-mode control and neural network (NN) design is presented. Design is performed by applying an NN to minimize the cost function that is selected to depend on the distance from the sliding-mode manifold, thus providing that the NN controller enforces sliding-mode motion in a closed-loop system. It has been proven that the selected cost function has no local minima in controller parameter space, so under certain conditions, selection of the NN weights guarantees that the global minimum is reached, and then the sliding-mode conditions are satisfied; thus, closed-loop motion is robust against parameter changes and disturbances. For controller design, the system states and the nominal value of the control input matrix are used. The design for both multiple-input-multiple-output and single-input-single-output systems is discussed. Due to the structure of the (M)ADALINE network used in control calculation, the proposed algorithm can also be interpreted as a sliding-mode-based control parameter adaptation scheme. The controller performance is verified by experimental results

Sliding mode and shaped input vibration control of flexible systems

Copyright [2008] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.In this paper, the vibration reduction problem is investigated for a flexible spacecraft during attitude maneuvering. A new control strategy is proposed, which integrates both the command input shaping and the sliding mode output feedback control (SMOFC) techniques. Specifically, the input shaper is designed for the reference model and implemented outside of the feedback loop in order to achieve the exact elimination of the residual vibration by modifying the existing command. The feedback controller, on the other hand, is designed based on the SMOFC such that the closed-loop system behaves like the reference model with input shaper, where the residual vibrations are eliminated in the presence of parametric uncertainties and external disturbances. An attractive feature of this SMOFC algorithm is that the parametric uncertainties or external disturbances of the system do not need to satisfy the so-called matching conditions or invariance conditions provided that certain bounds are known. In addition, a smoothed hyperbolic tangent function is introduced to eliminate the chattering phenomenon. Compared with the conventional methods, the proposed scheme guarantees not only the stability of the closed-loop system, but also the good performance as well as the robustness. Simulation results for the spacecraft model show that the precise attitudes control and vibration suppression are successfully achieved

Fast Adaptive Robust Differentiator Based Robust-Adaptive Control of Grid-Tied Inverters with a New L Filter Design Method

In this research, a new nonlinear and adaptive state feedback controller with a fast-adaptive robust differentiator is presented for grid-tied inverters. All parameters and external disturbances are taken as uncertain in the design of the proposed controller without the disadvantages of singularity and over-parameterization. A robust differentiator based on the second order sliding mode is also developed with a fast-adaptive structure to be able to consider the time derivative of the virtual control input. Unlike the conventional backstepping, the proposed differentiator overcomes the problem of explosion of complexity. In the closed-loop control system, the three phase source currents and direct current (DC) bus voltage are assumed to be available for feedback. Using the Lyapunov stability theory, it is proven that the overall control system has the global asymptotic stability. In addition, a new simple L filter design method based on the total harmonic distortion approach is also proposed. Simulations and experimental results show that the proposed controller assurances drive the tracking errors to zero with better performance, and it is robust against all uncertainties. Moreover, the proposed L filter design method matches the total harmonic distortion (THD) aim in the design with the experimental result

Modified Nonlinear Integral Sliding Mode Control for Satellite Attitude Stabilization Using Magnetically Suspended Gimbaled Momentum Wheel

This paper treats the attitude stabilization problem for satellite using only one MSGMW (Magnetically Suspended Gimbaled Momentum Wheel). To start, the coupled dynamic model of satellite and MSGMW is defined and simplified based on the fact that the attitude errors are small during the mission mode that the MSGMW services. In order to improve the dynamic performance, reduce the steady state error and avoid the chattering phenomenon, a modified integral chattering-free sliding mode controller with a nonlinear integral function and a saturation function is introduced. Lyapunov theory is employed to prove the convergence characteristic outside the boundary layer and the terminal convergence characteristic inside the boundary layer. A numerical simulation example is employed to show the effectiveness and suitability of the proposed controller

Terminal sliding mode control strategy design for second-order nonlinear system

This study mainly focuses on the terminal sliding mode control (TSMC) strategy design, including an adaptive terminal sliding mode control (ATSMC) and an exact-estimator-based terminal sliding mode control (ETSMC) for second-order nonlinear dynamical systems. In the ATSMC system, an adaptive bound estimation for the lump uncertainty is proposed to ensure the system stability. On the other hand, an exact estimator is designed for exact estimating system uncertainties to solve the trouble of chattering phenomena caused by a sign function in ATSMC law in despite of the utilization of a fixed value or an adaptive tuning algorithm for the lumped uncertainty bound. The effectiveness of the proposed control schemes can be verified in numerical simulations.<br /