Order Adaptive Control Research Articles

Disturbance rejection speed sensorless control of PMSMs based on full order adaptive observer

Speed sensorless control systems with a full order adaptive observer of the permanent magnet synchronous motor (PMSM) have received wide attention due to their advantages of simple structure, easy implementation and strong universality. However, they are sensitive to the load disturbances, which affects the speed performance of the control system. To solve this problem, this paper presents a disturbance rejection speed sensorless control of PMSMs based on full order adaptive observer to improve robustness against load disturbances. A load disturbance observer (LDO) is used to observe load disturbances, which feed-forward compensates the q-axis current to reduce the speed drop and accelerate the recovery time. Experimental results show that the proposed method has better anti-interference capability than full order adaptive speed sensorless control under the same steady-state performance.

Using the fractional order calculus in the combination of the MIT and Lyapunov stability method

AbstractThe main idea of the current paper consists in introducing the fractional order calculus in a control system. To control the system, an adaptive control technique with reference model is used. The fractional order models for the plant and reference model are obtained. To achieve the performances imposed by the fractional order reference model, a fractional order adaptive control law is proposed, which is a combination of two methods (MIT and Lyapunov stability). The original contribution in this paper is the use of fractional order calculus in the combined MIT and Lyapunov stability method and showing the dynamic behavior of the system. Several simulations are used to emphasize the effectiveness and benefits of the proposed method.

Direct fractional order MRAC adaptive control design for a class of fractional order commensurate linear systems

In this paper, we introduce a direct fractional order adaptive control design based on model reference adaptive control (MRAC) structure for a class of commensurate fractional order linear systems with an arbitrary relative degree, and whose parameters are unknown. By generalising the application of standard direct MRAC strategy to plants described by fractional order models, we develop a fractional adaptive control scheme (FOMRAC) based on the output feedback. We also define an adaptation control law ensuring the stability of the closed-loop system and the good tracking of the reference trajectory. The asymptotic stability of the fractional order control system is proven using an extension of the Lyapunov theorem. Simulation results show the effectiveness of the proposed control method even for plants with model parametric variations and additive noises.

H ∞ Time-Delayed Fractional Order Adaptive Sliding Mode Control for Two-Wheel Self-Balancing Vehicles.

In this paper, a time-delayed fractional order adaptive sliding mode control algorithm is proposed for a two-wheel self-balancing vehicle system. The closed-loop system is proved based on the Lyapunov-Razumikhin function. The switching function is designed to make the system robust when facing uncertainties and external disturbances. It is designed to avoid monotonically increasing gains and can handle state-dependent uncertainties without a prior bound. The two-wheel self-balancing vehicle used in the experiment consists of a gyroscope MPU-6050 and accelerometer, a motor driving circuit composed of a motor driving chip TB6612FNG, and STM32F103x8B that is selected as the control core. The experimental results show that the time-delayed fractional order adaptive sliding mode control algorithm can make the vehicle achieve autonomous balance and quickly restore its stable state while appropriate disturbance is introduced.

Fractional order adaptive MRAC controller for an active suspension system

This paper investigates the use of fractional order operators in conventional model reference adaptive control (MRAC). A fractional adaptive controller is designed based on the use of a fractional-order parameter adjustment rule. Applied in numerical simulations for an active suspension system and compared with the conventional MRAC, it is shown that the performances of FOMRAC are superior to classical control schemes.

Robust MRAC-based adaptive control of a Doubly Fed Induction Generator (DFIG) in a Wind energy system using a fractional order Integrator

This paper presents a robust control of doubly fed induction generator for wind generation system. The whole system is presented in d-q-synchronous reference frame. We propose the implementation of adaptive control with integer model reference MRAC, fractional model reference FOMRAC with integer and fractional order control law design for active and reactive power supervision control in the doubly fed induction generator (DFIG) for wind energy systems. The objective is to realize a comparative study between the classical regulator MRAC and the proposed FO-MRAC with integer and fractional order control law in order to demonstrate the robustness of the fractional order adaptive control with fractional order integral in control law comparatively to integer order one. Performance and robustness results obtained will be presented and analyzed.

Design of Adaptive Fuzzy Controllers for a Class of Fractional Order Nonlinear MIMO Systems With Input Saturation

This paper develops a fractional order adaptive fuzzy backstepping control scheme for an incommensurate fractional order uncertain nonlinear multiple-input multiple-output (MIMO) systems with external disturbance and input saturation. Combined with the adaptive and backstepping technique, the fuzzy logic system is used to approximate the unknown nonlinear uncertainties in each step of the backstepping, and the incommensurate fractional order parameters update laws for fuzzy logic system, unknown parameters as well as the external disturbances are proposed in the controller to compensate the unknown nonlinearities, unknown parameters and disturbances. With the aids of the frequency distributed model of fractional integrator for the fractional order systems in the procedure of controller design, the stability of the closed loop system is established. At last, two simulation examples are demonstrated to verify the robustness and effectiveness of the proposed controller.

Mixed Fractional Order Adaptive Control: Theory and Applications

Abstract In this paper we study the adaptive control problem of integer order plants using fractional order adaptive laws in the controller. The study is based on a general methodology developed recently to establish boundeness and asymptotic behavior of solutions to multi-order systems (set of differential equations with different derivation orders) having multiple time-varying delays. Also it is based on recent results for fractional order systems under the perspective of the so called ”Error Models”. The method relies on vector Lyapunov-like functions and on comparison arguments. Boundedness and convergence of the solutions are theoretically analyzed and applications to fractional adaptive schemes are presented towards the end of the paper, including numerical simulations to verify the analytical results.

Time-varying parameter model reference adaptive control and its application to aircraft

A new Second Order (SO) adaptive control approach, that accounts for both matched and unmatched unknown time-varying uncertainties, is proposed in this paper. It is developed based on the Predictor based Model Reference Adaptive Control (PMRAC) structure. In this approach, the estimated parameter dynamics is composed of a σ-modified PMRAC update law and a predicted parameter dynamics, with projection operator. The predicted parameter dynamics consists of a stable known eigendynamics, a feedback of an approximate parameter error, and the remaining part linearly parameterized by a set of known regressor functions combined with an adaptive estimate of unknown second-order parameters, which are updated by a Lyapunov design. Due to the estimation of time derivatives of the parameters, the proposed predictor based SO-MRAC is hence capable of capturing the rapid parameter variations in system dynamics. Furthermore, a generalized ultimate boundedness formulation based on the Lyapunov theory is presented for its stability analysis. This formulation provides separate bounds for each of the state vector partitions, mainly tracking and parameter estimation errors. Finally, this proposed approach is applied to control of lateral dynamics of an unmanned aircraft to illustrate the usefulness of the proposed approach. The simulation results are found to be quite satisfactory both in terms of tracking and adaptation performance.

A HTF-Based Higher-Order Adaptive Control of Single-Stage Grid-Interfaced PV System

In this paper, a hyperbolic tangent function (HTF) based higher order adaptive control algorithm is used with perturb & observe based maximum power point tracking algorithm for a three-phase, single-stage, grid-interfaced solar photovoltaic system with distribution static compensator capabilities. The variable learning based HTF control algorithm is used for the reduction of the mean square error and increases the tracking speed in the system, thereby improving the response of the system. The HTF-based control algorithm is simple in implementation with easy mathematical formulations. The proposed system is simulated in MATLAB/Simulink and is tested on a developed prototype in the laboratory under various abnormal conditions, such as variable solar irradiation, load unbalancing, and voltage sag/swell. The response of system is satisfactory and the total harmonic distortions of grid current are within the limit, as outlined in the IEEE-519 standard.

Fractional Order Adaptive Sliding Mode Control System of Micro Gyroscope

In this paper, an adaptive sliding mode control method based on fractional order method is proposed for the estimation of unknown parameters in micro gyroscope system. Firstly, compared with the traditional integer order sliding surface, the fractional order sliding surface in this paper increases the order terms which can adjust the fractional order, and improve the control performance and precision. Additionally, the adaptive laws are derived to tune the control parameters online based on the Lyapunov stability theorem to deal with the uncertainty of the system. Moreover, simulation results show that the proposed control system's convergence speed, output signal tracking error and parameter fitting are better than the integral sliding mode control system, proving that the proposed control method is practicable and effective.

Two Novel Approaches of NTSMC and ANTSMC Synchronization for Smart Grid Chaotic Systems

The presence of uncertainties and external disturbances is one of the unavoidable problems with various practical systems which might be unavailable in real-time. Sliding Mode Control (SMC) is one of the effective robust control methods to deal with these uncertainties and external disturbances. In this paper, two novel controllers are designed by using Nonsingular Terminal SMC (NTSMC) and Adaptive Nonsingular Terminal SMC (ANTSMC) methods for synchronization of dual smart grid chaotic systems with various uncertainties and external disturbances. Indeed, both adaptive and non-adaptive controllers based on NTSMC are proposed to provide two alternatives which can adjust by changing operating conditions and dynamics. The concept of SMC method guarantees controller robustness against various uncertainties and external disturbances. Elimination of the undesirable chattering phenomenon is addressed in this study which is one of the common deficiencies with conventional SMC method. Additionally, finite time concept is used to speed up the convergence rate. Finite time stability proof is performed by using Lyapunov stability theory. The numerical simulation is carried out in Simulink/MATLAB to reveal the validity of the proposed controllers for the smart grid chaotic system. A comprehensive comparison is made by performing simulation for the Fractional Order Adaptive Sliding Mode Control (FOASMC) controller and defining three performance criteria, among the proposed controllers in this study and FOASMC controller.

Fractional Order Adaptive Sliding Mode Control for the Deployment of Space Tethered System With Input Limitation

This paper develops a novel sliding mode control strategy for the deployment of space tethered system with consideration of constrained input. The simplified nonlinear dynamic model of space tethered system in elliptical orbits is first modeled by using the Euler–Lagrange mechanical equation. Considering the flexibility of tether, the compression or any component of shear forces for the tether is assumed to be input limitation. By introducing fractional order operator and saturation function into the sliding surface, a new adaptive fractional order sliding mode control strategy is introduced based on the proposed nonlinear dynamic model. Compared with classical sliding mode methods, a faster deployment time without overshoot and chattering-reduced performance can be achieved. Finally, numerical simulations are illustrated to validate the effectiveness of our methods.

Adaptive Backstepping State Feedback Control for Fractional Order Systems with Input Saturation

In this paper, we propose a fractional order adaptive backstepping control solution to the saturation problem of incommensurate fractional order system with uncertainty and non-linearity. A model transformation is introduced to make the system appropriate to backstepping scheme, and the virtual signals are generated to compensate saturation via the construction of fractional order auxiliary system. By indirect Lyapunov method, the backstepping procedure is applied to fractional order systems with input saturation for the first time, which achieves the goals of stabilization and tracking. Finally, the effectiveness of the proposed fractional order backstepping is demonstrated in several examples.

Robust Tracking Control of Networked Control Systems With Communication Constraints and External Disturbance

This paper addresses the problem of robust tracking control of networked control systems with communication constraints (network-induced delay, packet dropouts, and packet disorder) and external disturbance. A novel networked predictive control algorithm based on k -order adaptive discrete-time sliding-mode control ( k -ADSMC) is proposed. The ADSMC, which can self-adapting adjust sliding-mode parameters and ensure faster convergence, is designed based on the error and error difference of tracking output. Furthermore, k -ADSMC is designed, which uses the estimated disturbance as weight factors and synthesizes the sliding- mode values of all k times, in order to improve the robust of tracking control. Finally, the stability of the system is proved, and a dc motor servo system is utilized to verify the effectiveness of the proposed method.

Adaptive backstepping control for fractional order systems with input saturation

A fractional order adaptive backstepping control scheme is presented for an incommensurate fractional order systems in the presence of input saturation. In order to compensate the saturation, the necessary signals are generated by constructing a fractional order auxiliary system. Besides the nonlinear functions and unknown parameters of systems, the uncertainties, especially the unknown control input coefficient, are emphasized here. The adoption of fractional order parameters update law and nonlinear feedback has added more degree of freedom to controllers, which leads to a larger range of application. The frequency distributed model is introduced so that the indirect Lyapunov method is available in the procedure of controller design. All the differential signals, used for the control and estimation, are obtained through fractional order tracking differentiator. Compared with previous methods, the backstepping method is first adopted to solve the saturation problem of incommensurate order systems with nonlinearities and uncertainties, which achieves stabilization and tracking. To highlight the effectiveness of the proposed controller, simulation examples are demonstrated at last.

Robust DC-motor speed control using a fractional adaptive PI<SUP align="right">α</SUP> regulator

Conventional adaptive PI controller is one of the most widely used controllers in industry, but the recent advancement in fractional calculus has introduced applications of fractional order calculus in control theory. One of the prime applications of fractional calculus is fractional adaptive PI controller and it has received a considerable attention in academic studies and in industrial applications. Fractional order adaptive PI controller is an advancement of classical integer order adaptive PI controller. In many a cases fractional order adaptive PI controller has outperformed classical integer order adaptive PI controller. Particularly for the problem of controlling the speed of DC-motors, it is very important use a suitable and efficient controller as any small change can lead to instability of the closed loop system. This research paper, studies the control aspect of fractional order controller in speed control of DC motor. A comparative study of classical adaptive PI controller and fractional order adaptive PI controller has been performed to illustrate the effectiveness and robustness of the proposed fractional adaptive control solution.

Optimal fractional order adaptive controllers for AVR applications

This work presents strategies for fractional order model reference adaptive control (FOMRAC) and fractional order proportional–integral–derivative control (FOPID) applied to an automatic voltage regulator (AVR). The paper focuses on tuning the gains and orders of the FOPID controller and the gains and orders adaptive laws of the FOMRAC controller, with the goal of minimizing non-linear and high dimensionality objective functions, using sequential quadratic programming (SQP), particle swarm optimization (PSO), and genetic algorithms (GA). Two models used for AVR have been studied and reported in the literature and are the bases of the three case studies reported in this paper. To analyze the advantages and disadvantages of the proposed MRAC, comparisons are made with the previous results, i.e. with the results obtained by a PID controller and an MRAC controller optimized by GA. We demonstrate through some performance criteria that fractional order controllers optimized by the PSO algorithm improve the behavior of the controlled system, specifically the robustness with respect to model uncertainties, and improvements with respect to the speed convergence of the signals.

Artificial Intelligence Based First Order Adaptive Sliding Mode Controller for Position Control of a DC Motor Actuator

This paper presents an Artificial Intelligence (AI) based approach uniquely applied to Permanent Magnet DC motor actuator for position control. The AI method employed in this work is Fuzzy logic. A first order lag Sliding mode controller is tuned and combined with an Adaptive Fuzzy- PI controller architecture which operates in parallel. The controller architecture proposed in this study is aimed at improving the disturbance rejection capability, steady state as well as transient performance of the conventional Adaptive Fuzzy-PI controller and sliding mode controller. Hence, the robust control law of the proposed controller (SM+FZ-PI) consists of a discontinuous Sliding mode output added to a continuous Adaptive Fuzzy-PI controller output. The sliding mode controller switches on only when disturbance in the system is detected. The performance of the proposed controller architecture has been compared with a conventional PID and Adaptive Fuzzy-PI controllers for performance evaluation with respect to several operating conditions such as load torque disturbance injection, noise injection in feedback loop, motor non-linearity exhibited by parameters variation, and a step change in reference input demand. The proposed controller (SM+FZ-PI), had the best disturbance rejection and steady state error elimination.

Adaptive backstepping output feedback control for a class of nonlinear fractional order systems

This article presents a novel fractional order adaptive backstepping output feedback control scheme for nonlinear fractional order systems. The needed feedback information is constructed via a state estimation filter. To improve the control performance, tracking differentiators, nonlinear elements and fractional order update laws were introduced and applied to the control systems. With the aids of this frequency distribute model and the indirect Lyapunov method, the stability and the tracking convergence of the resulting closed-loop system were established. A careful simulation study was provided to illustrate the effectiveness of this novel scheme.