Adaptive Non-Linear High Gain Observer Based Sensorless Speed Estimation of an Induction Motor

International audienc

Lyapunov-based Control Design For Uncertain Mimo Systems

In this dissertation. we document the progress in the control design for a class of MIMO nonlinear uncertain system from five papers. In the first part, we address the problem of adaptive control design for a class of multi-input multi-output (MIMO) nonlinear systems. A Lypaunov based singularity free control law, which compensates for parametric uncertainty in both the drift vector and the input gain matrix, is proposed under the mild assumption that the signs of the leading minors of the control input gain matrix are known. Lyapunov analysis shows global uniform ultimate boundedness (GUUB) result for the tracking error under full state feedback (FSFB). Under the restriction that only the output vector is available for measurement, an output feedback (OFB) controller is designed based on a standard high gain observer (HGO) stability under OFB is fostered by the uniformity of the FSFB solution. Simulation results for both FSFB and OFB controllers demonstrate the efcacy of the MIMO control design in the classical 2-DOF robot manipulator model. In the second part, an adaptive feedback control is designed for a class of MIMO nonlinear systems containing parametric uncertainty in both the drift vector and the input gain matrix, which is assumed to be full-rank and non-symmetric in general. Based on an SDU decomposition of the gain matrix, a singularity-free adaptive tracking control law is proposed that is shown to be globally asymptotically stable (GAS) under full-state feedback. iii Output feedback results are facilitated via the use of a high-gain observer (HGO). Under output feedback control, ultimate boundedness of the error signals is obtained the size of the bound is related to the size of the uncertainty in the parameters. An explicit upper bound is also provided on the size of the HGO gain constant. In third part, a class of aeroelastic systems with an unmodeled nonlinearity and external disturbance is considered. By using leading- and trailing-edge control surface actuations, a full-state feedforward/feedback controller is designed to suppress the aeroelastic vibrations of a nonlinear wing section subject to external disturbance. The full-state feedback control yields a uniformly ultimately bounded result for two-axis vibration suppression. With the restriction that only pitching and plunging displacements are measurable while their rates are not, a high-gain observer is used to modify the full-state feedback control design to an output feedback design. Simulation results demonstrate the ef cacy of the multi-input multioutput control toward suppressing aeroelastic vibration and limit cycle oscillations occurring in pre and post utter velocity regimes when the system is subjected to a variety of external disturbance signals. Comparisons are drawn with a previously designed adaptive multi-input multi-output controller. In the fourth part, a continuous robust feedback control is designed for a class of high-order multi-input multi-output (MIMO) nonlinear systems with two degrees of freedom containing unstructured nonlinear uncertainties in the drift vector and parametric uncertainties in the high frequency gain matrix, which is allowed to be non-symmetric in general. Given some mild assumptions on the system model, a singularity-free continuous robust tracking coniv trol law is designed that is shown to be semi-globally asymptotically stable under full-state feedback through a Lyapunov stability analysis. The performance of the proposed algorithm have been verified on a two-link robot manipulator model and 2-DOF aeroelastic model

Continuous observer design for a class of multi-output nonlinear systems with multi-rate sampled and delayed output measurements

In this paper, continuous observer is designed for a class of multi-output nonlinear systems with multirate sampled and delayed output measurements. The time delay may be larger or less than the sampling intervals. The sampled and delayed measurements are used to update the observer whenever they are available. Sufficient conditions are presented to ensure global exponential stability of the observation errors by constructing a Lyapunov–Krasovskii function. A numerical example is given to illustrate the effectiveness of the proposed methods.http://www.elsevier.com/locate/automatica2018-01-31hb2017Electrical, Electronic and Computer Engineerin

Adaptive neural control of MIMO nonlinear systems with a block-triangular pure-feedback control structure

This paper presents adaptive neural tracking control for a class of uncertain multi-input-multi-output (MIMO) nonlinear systems in block-triangular form. All subsystems within these MIMO nonlinear systems are of completely nonaffine purefeedback form and allowed to have different orders. To deal with the nonaffine appearance of the control variables, the mean value theorem (MVT) is employed to transform the systems into a block-triangular strict-feedback form with control coefficients being couplings among various inputs and outputs. A systematic procedure is proposed for the design of a new singularityfree adaptive neural tracking control strategy. Such a design procedure can remove the couplings among subsystems and hence avoids the possible circular control construction problem. As a consequence, all the signals in the closed-loop system are guaranteed to be semiglobally uniformly ultimately bounded (SGUUB). Moreover, the outputs of the systems are ensured to converge to a small neighborhood of the desired trajectories. Simulation studies verify the theoretical findings revealed in this work

Asymptotic Tracking Control of Uncertain MIMO Nonlinear Systems with Less Conservative Controllability Conditions

For uncertain multiple inputs multi-outputs (MIMO) nonlinear systems, it is nontrivial to achieve asymptotic tracking, and most existing methods normally demand certain controllability conditions that are rather restrictive or even impractical if unexpected actuator faults are involved. In this note, we present a method capable of achieving zero-error steady-state tracking with less conservative (more practical) controllability condition. By incorporating a novel Nussbaum gain technique and some positive integrable function into the control design, we develop a robust adaptive asymptotic tracking control scheme for the system with time-varying control gain being unknown its magnitude and direction. By resorting to the existence of some feasible auxiliary matrix, the current state-of-art controllability condition is further relaxed, which enlarges the class of systems that can be considered in the proposed control scheme. All the closed-loop signals are ensured to be globally ultimately uniformly bounded. Moreover, such control methodology is further extended to the case involving intermittent actuator faults, with application to robotic systems. Finally, simulation studies are carried out to demonstrate the effectiveness and flexibility of this method

A Model-Free Control System Based on the Sliding Mode Control Method with Applications to Multi-Input-Multi-Output Systems

In this work, a model-free sliding mode control technique for linear and nonlinear uncertain multi-input multi-output systems is proposed. The developed method does not require a mathematical model of the dynamic system. Instead, knowledge of the system’s order, state measurements, and control input gain matrix shape and bounds are assumed to develop the control law and drive the system’s states to track a desired trajectory. The control system relies on estimating the error between previous and current control inputs to stabilize the system. Lyapunov’s stability criterion is used in the derivation process to ensure closed-loop asymptotic stability. High frequency chattering of the control input and higher-order states, often observed with the sliding mode control method, is eliminated using a smoothing boundary layer. Simulations are performed on a variety of linear and nonlinear systems, including a quadrotor model, to test the performance of the control law. Finally, the model-free sliding mode control system is modified to account for the effects of actuator time-delays

A Model-Free Control System Based on the Sliding Mode Control with Automatic Tuning Using as On-Line Parameter Estimation Approach

The sliding mode control algorithm and Lyapunov-based methods, have received much attention recently due to their ability to directly handle nonlinear systems while guaranteeing closed-loop tracking stability. In this work, a unique model-free sliding mode control technique has developed solely based on previous control inputs. The new method requires only knowledge of the system order and state measurements and does not require a theoretical model of the dynamic system. Lyapunov’s stability theorem is used in the controller formulation process to ensure closed-loop asymptotic stability. High frequency chattering of the control effort is reduced by using a smoothing boundary layer into the control law. Parameters variation during control operating and noise effect cannot be handled by the model-free controller if the controller tuning parameters are chosen arbitrarily since tracking performance becomes unacceptable. In addition, in previous work, the bounds of the input influence gain parameters were assumed to be known to derive the model-free controller. Therefore, in this work, a new approach is proposed for estimating the increment to the switching gain in real-time to ensure the sliding condition (which guarantees closed-loop tracking stability) is satisfied using a control law form that assumes a strictly unitary input influence gain. In formulation of estimation law, an exponential forgetting factor is combined with the least-squares estimator to ensure the updated data are used and past data are excluded. An automatic bounded forgetting tuning technique is developed to maintain the benefits of data forgetting while avoiding the possibility of gain unboundedness in absence of persistent excitation. The tuning estimator is assured that the resulting gain matrix is upper bounded regardless of the persistent excitation by suspending the data forgetting if the gain matrix reaches the specified upper bound. Simulations are performed on a series of linear and nonlinear SISO and MIMO systems with and without including actuator time-delay effects. Finally, a model is developed to simulate a quadcopter as a real-world application case. In all cases, the controller achieved perfect or near-perfect tracking performance using updated controller and on-line estimator tuning process