Robust Direct Adaptive Control Research Articles

Practical adaptive robust tracking control of the dual-valve parallel electro-hydraulic servo system with reduced-order model

To meet the increasing demand for trajectory tracking accuracy and high-efficiency requirements in modern mobile machinery, this paper proposes a practical adaptive robust control method based on the dual-valve parallel electro-hydraulic servo system. Existing tracking control strategies for such servo systems rely on a backstepping method and assume that full states are known, which is stringent in practice. To cope with the problem, we reduce the mathematical model order of the studied system using singular perturbation theory in this paper, and only the position feedback is required for the control implementation. Then, to achieve high accuracy tracking control, a direct adaptive robust control scheme combing with a dynamic flow allocation layer is adopted to synthesize the controller. With this method, parameter uncertainties and load disturbance are rejected, and valve characteristics are considered in the dynamic flow allocation layer to solve the flow redundancy problem, respectively. Convergence of the simplified system tracking results is proved theoretically. Extensive co-simulations and experimental tests are carried out to illustrate the effectiveness of the proposed strategy, both tracking precision and flow distribution can be achieved efficiently by simple parameter adjustments in the field.

A composite adaptive robust control for pneumatic servo systems with time-varying inertia

This article proposes a composite adaptive robust control for a pneumatic servo system with time-varying inertia to achieve a good tracking performance. The proposed design not only preserves the merits of both direct adaptive robust control and indirect adaptive robust control but also obtains a better performance of the working condition with time-varying inertias. Firstly, prescribed tracking performance is guaranteed without knowing the bounds of parametric and non-parametric uncertainties by leveraging a discontinuous projection and deterministic robust control technique. And a nonlinear tracking differentiator is used to obviate differential signal in backstepping. Secondly, the online parametric estimation algorithm is developed by intelligently integrating tracking error dynamics and physical plant dynamics. By effectively using the information of both tracking error and prediction error, a high adaptation gain can be used for achieving a faster parameter convergence and smaller tracking error. Moreover, exponential convergence of both tracking error and prediction error can be obtained under certain conditions. Lastly, comparative experiments on different conditions are carried out for a single-rod pneumatic cylinder driven by a proportional directional valve to demonstrate the superiority of the proposed method.

Robust attitude control of the three-dimensional unknown chaotic satellite system

This paper proposes a novel continuous-time robust direct adaptive controller for the attitude control of the three-dimensional unknown chaotic spacecraft system. It considers that the plant’s nonlinear terms, exogenous disturbances, and model uncertainties are unknown and bounded; the controller design is independent of the system’s nonlinear terms. These controller attributes flourish the robust performance of the closed-loop and establish smooth state vector convergence to zero. The proposed controller consists of three parts: (1) a linear controller establishes the stability of the closed-loop at the origin, (2) a nonlinear controller component that autonomously adjusts the feedback gain, and (3) a nonlinear adaptive controller compensates for the model uncertainties and external disturbances using the online estimates of bounds and model uncertainties. The output of this part remains within a given upper and lower bound. The feedback controller gain is large when the state variables are away from the origin and become small in the origin’s vicinity. This feature is novel and contributes to the synthesis of smooth control effort that establishes robust fast and oscillation-free convergence of the state variables to zero. The Lyapunov direct stability analysis assures the global asymptotic robust stability of the closed-loop. Computer simulations and comparative analysis are included to verify the theoretical findings.

A Lyapunov-based direct adaptive controller for the suppression and synchronization of a perturbed nuclear spin generator chaotic system

This article designs and synthesizes a new Lyapunov-based robust direct-adaptive controller (RDAC) and investigates the control and synchronization of chaos in the nuclear spin generator chaotic (NSGC) system. The inevitable time-varying external disturbances and model uncertainties perturb the NSGC system. The nonlinear terms, external disturbances, model uncertainties, and plant's parameters are unknown and bounded. Avoiding the cancelation of the nonlinear terms of the plant by the controller makes the closed-loop robust stable in the presence of unknown parametric uncertainties; this concept blooms base for efficient control law design. The proposed RDAC eradicates the effects of the time-varying unknwon external disturbances and model uncertainties and accomplishes quick and smooth convergence of the state varaible (error vector) trajectories to the origin with reduced oscillations. Based on the Lyapunov function principle, the article describes a detailed analysis of the closed-loop stability. It provides suitable adaptive laws that estimate the upper bound of unknown controller parameters, external disturbances, and model uncertainties. The computer simulation results endorse the theoretical analysis, and the comparative study highlights the benefits.

Neural network–based direct adaptive robust control of unknown MIMO nonlinear systems using state observer

SummaryThis paper focuses on the problem of adaptive robust tracking control for a class of uncertain multiple‐input and multiple‐output (MIMO) nonlinear system. Unlike most previous research studies, model dynamics, disturbances, and state variables are unknown in this paper. A novel observer‐based direct adaptive neuro‐sliding mode control approach is proposed of which the only required knowledge is the system output. By incorporating the Adaptive Linear Neuron (ADALINE) neural network (NN) into the conventional sliding mode observer, the proposed observer has favorable performance. In the controller, a radial basis function (RBF) NN is constructed to approximate the unknown equivalent control laws and the estimation of the sliding surface is applied as the input. A gain‐adaptation sliding mode term is designed to enhance the robustness of the control system. Besides, the free parameters of the ADALINE NN and the RBFNN are updated online by adaptive laws to obtain optimal approximation performance. Finally, the comparative simulations are given to show the effectiveness and merits of proposed scheme.

Robust Direct Adaptive Controller Design for Photovoltaic Maximum Power Point Tracking Application

Tracking the maximum output power of a photovoltaic (PV) cell is an important problem to harvest more energy at different weather and load conditions. This paper presents the design and simulation of a robust direct adaptive controller (RDAC) for maximum power point tracking (MPPT) device based on boost converter topology. A mathematical model is developed, and a suitable RDAC is designed for MPPT device, and simulations are performed using MATLAB/Simulink to verify the controller’s robustness at varying operating conditions. The real-time irradiance and temperature data are used on an hourly basis to test the suggested MPPT adaptive controller for a typical sunny day in summer and winter. The simulation results show that the RDAC performs excellent tracking under varying conditions such as irradiance, temperature, load, boost converter inductance, and capacitance.

A robust direct adaptive fuzzy control for a class of uncertain nonlinear MIMO systems

A robust direct adaptive fuzzy controller for a class of MIMO nonlinear systems with uncertainties and external disturbances is presented. The robust adaptive fuzzy controller is successfully employed using tracking error universe. Also adaption laws of the proposed controller are developed such that to be guaranteed the steady constant of the adjustable parameters and the estimated bound of the uncertainties and approximation error without utilizing any modification algorithm. Stability of the proposed method, i.e., uniformly ultimately boundedness of the tracking error and all involved signals, is shown based on Lyapunov theory. Simulation results demonstrate the capability and efficiency of the proposed technique for controlling nonlinear systems with uncertainties and external disturbances.

Direct adaptive robust tracking control for 6 DOF industrial robot with enhanced accuracy

A direct adaptive robust tracking control is proposed for trajectory tracking of 6 DOF industrial robot in the presence of parametric uncertainties, external disturbances and uncertain nonlinearities. The controller is designed based on the dynamic characteristics in the working space of the end-effector of the 6 DOF robot. The controller includes robust control term and model compensation term that is developed directly based on the input reference or desired motion trajectory. A projection-type parametric adaptation law is also designed to compensate for parametric estimation errors for the adaptive robust control. The feasibility and effectiveness of the proposed direct adaptive robust control law and the associated projection-type parametric adaptation law have been comparatively evaluated based on two 6 DOF industrial robots. The test results demonstrate that the proposed control can be employed to better maintain the desired trajectory tracking even in the presence of large parametric uncertainties and external disturbances as compared with PD controller and nonlinear controller. The parametric estimates also eventually converge to the real values along with the convergence of tracking errors, which further validate the effectiveness of the proposed parametric adaption law.

LMI-based design of a robust direct adaptive attitude control for a satellite with uncertain parameters

Three axes attitude control of CNES microsatellite is considered. The satellite has uncertain inertia, natural frequency and damping. Satellite dynamics are modelized using descriptor form, with matrices affinely dependent on the uncertain parameters. LMI-based methods using S-variables allow to design a robust adaptive controller with tunable gain adaptation parameters. Illustrated simulations show that the controller stabilizes the satellite with any inertia physically acceptable. Theoretical results can be applied to any descriptor system rational in the uncertainties.

A new and robust control strategy for a class of nonlinear power systems: Adaptive general type-II fuzzy

In this article, a robust direct adaptive general type-2 fuzzy logic controller is introduced for a class of nonlinear power systems. The proposed controller uses the advantages of general type-2 fuzzy logic system in handling dynamic uncertainties to approximate unknown nonlinear actions. Implementing general type-2 fuzzy system is computationally costly; however, by using a recently introduced α-plane representation, general type-2 fuzzy logic system can be seen as a composition of several interval type-2 fuzzy logic systems with a corresponding level of α for each. Linguistic rules are directly incorporated into the controller. In addition, an [Formula: see text] compensator is corrupted to attenuate external disturbance and fuzzy approximation error. General type-2 fuzzy adaptation laws are also derived using Lyapunov approach. It is worth noting that mathematical analysis proves the stability of the closed-loop system. In order to evaluate the performance of the proposed controller, the results are compared with those obtained by direct adaptive type-1 fuzzy logic controller, a direct adaptive interval type-2 fuzzy logic controller and adaptive proportional–integral–derivative, which are the latest researches in the problem in hand. The proposed controller is applied to a chaotic power system as a case study. Simulation reveals the effectiveness of the proposed controller in presence of dynamic uncertainties and external disturbances.

The Simplicity of Robust Direct Adaptive Control with Disturbance Rejection for Linear Infinite-Dimensional Systems: An Introduction

Our purpose in this paper is to provide an introduction to direct adaptive control in infinite dimensions and to prove the remarkable simplicity of infinite dimensional adaptive control even in infinite dimensions. However, we will show that the mathematical foundations are much more stringent in infinite dimensional theory. Consequently, this paper will emphasize some important fundamentals and will not be comprehensive. Much more can be done, but here we hope to provide a starting point for further exploration. Given a linear continuous-time infinite-dimensional plant on a Hilbert space and disturbances of known and unknown waveform, we show that there exists a very simple stabilizing direct adaptive control law with certain disturbance rejection and robustness properties. The closed loop system is shown to be exponentially convergent to a neighborhood with radius proportional to bounds on the size of the disturbance. The plant is described by a closed densely defined linear operator that generates a continuous semigroup of bounded operators on the Hilbert space of states. To illustrate the use of the control law, we apply the result to a partial differential equation example of an unstable diffusion system, but other applications are possible.

Global Task Coordinate Frame-Based Contouring Control of Linear-Motor-Driven Biaxial Systems With Accurate Parameter Estimations

This paper presents a global task coordinate frame (TCF) (GTCF)-based integrated direct/indirect adaptive robust contouring controller for linear-motor-driven biaxial systems that achieves both stringent contouring performance and accurate parameter estimations. In contrast to the past research works those use various locally defined TCFs “attached” to the desired contour to approximately calculate the contouring error for feedback controller designs, this paper first formulates the contouring control problem using a recently developed GTCF, in which calculation of the contouring error is rather accurate and not affected by the curvature of the desired contour. A physical-model-based indirect-type parameter-estimation algorithm is then synthesized to obtain accurate online estimates of unknown physical model parameters. An integrated direct/indirect adaptive robust controller with dynamic-compensation-type fast adaptation is also constructed to preserve the excellent transient and steady-state performance of the direct adaptive robust control (ARC) designs. Comparative experimental results show that the proposed GTCF-based integrated direct/indirect ARC algorithm not only achieves the best contouring performance but also possesses rather accurate estimations of physical parameters.

Indirect Adaptive Robust Control of Hydraulic Manipulators With Accurate Parameter Estimates

In a general direct adaptive robust control (DARC) framework, the emphasis is always on the guaranteed transient performance and accurate trajectory tracking in presence of uncertain nonlinearities and parametric uncertainties. Such a direct algorithm suffers from lack of modularity, controller-estimator inseparability, and poor convergence of parameter estimates. In the DARC design the parameters are estimated by gradient law with the sole purpose of reducing tracking error, which is typical of a Lyapunov-type design. However, when the controller-estimator module is expected to assist in secondary purposes such as health monitoring and fault detection, the requirement of having accurate online parameter estimates is as important as the need for the smaller tracking error. In this paper, we consider the trajectory tracking of a robotic manipulator driven by electro-hydraulic actuators. The controller is constructed based on the indirect adaptive robust control (IARC) framework with necessary design modifications required to accommodate uncertain and nonsmooth nonlinearities of the hydraulic system. The online parameter estimates are obtained through a parameter adaptation algorithm that is based on physical plant dynamics rather than the tracking error dynamics. While the new controller preserves the nice properties of the DARC design such as prescribed output tracking transient performance and final tracking accuracy, more accurate parameter estimates are obtained for prognosis and diagnosis purpose. Comparative experimental results are presented to show the effectiveness of the proposed algorithm.

Stability analysis of a combined direct and variable structure adaptive control

This study presents the proofs of robust stability of a direct adaptive controller with a variable structure (VS) parcel. The control law parameters are adjusted based on a method proposed by Narendra and Boskvic (1990). In this approach, two sets of parameters must be obtained. One set is used to attain the control objective which is, in this case, to track the output of a reference model as closely as possible. The other set is of VS type, which is used to improve performance and robustness. A slight modification of the adaptive law for the VS parameters with proofs of robust stability is proposed here. With this modified law, all mathematical proofs already existing in the literature for robust direct adaptive controllers can be extended to the case under study. The combined controller is applied to a single input single output linear time invariant (SISO LTI) plant with unmodelled dynamics of multiplicative and additive types. It is proven that the combined controller can arbitrarily improve the convergence of the error while keeping the system robustness, if compared to the non-combined case. Simulation results illustrate the efficiency of the proposed control strategy.

Robust direct adaptive controller for the nonlinear highway bridge benchmark

This paper presents a direct adaptive control scheme for the active control of the nonlinear highway bridge benchmark. The controller is based on the premise of direct adaptive control, where-in the system response is made to follow a desired trajectory. The principal problem of the unavailability of the correct network output is inferred from the observed structure behavior. The control force in this paper is calculated using a single hidden layer nonlinearly parameterized neural network in conjunction with a proportional-derivative type controller. The neural network is utilized to approximate the nonlinear control law, that is known to exist, and not the system nonlinearities. Stable tuning laws for the free parameters of the nonlinearly parameterized network are derived based on Lyapunov theory. Set in the framework of adaptive control, the proposed control architecture addresses important issues related to the stability of the closed loop system and parameter bounds. Performance of the proposed control scheme is evaluated on the recently proposed nonlinear highway bridge benchmark, incorporating nonlinear isolation bearings and nonlinear structural elements. Results are presented in terms of a well-defined set of performance indices. The results show that the proposed controller scheme can achieve good response reductions in the structure, without the need for the exact description of the nonlinearities, or extensive structural system information. Copyright © 2009 John Wiley & Sons, Ltd.

Stability and robustness analysis of MIMO MRAC using Kp = L 2 D 2 S 2 factorization

For a class of MIMO systems with input and output unmodeled dynamics, bounded disturbances and any relative degree, using the idea of Kp = L 2 D 2 S 2 factorization, the design and analysis of robust direct model reference adaptive control are further investigated in this article. By establishing the Lp and L 2δ relationship properties between the input and output, multivariable swapping lemmas and relating all the signals in the closed-loop system with the normalizing signal, stability and robustness of adaptive system are analyzed rigorously. Compared with the existing results, the proof procedure is more compact and simple. A simulation example verifies the effectiveness of the control scheme.

Robust direct adaptive fuzzy control for nonlinear MIMO systems

Abstract For a class of nonlinear multi-input multi-output systems with uncertainty, a robust direct adaptive fuzzy control scheme was proposed. The feedback control law and adaptive law for parameters were derived based on Lyapunov design approach. The overall control scheme can guarantee that the tracking error converges in the small neighborhood of origin, and all signals of the closed-loop system are uniformly bounded. The main advantage of the proposed control scheme is that in each subsystem only one parameter vector needs to be adjusted on-line in the adaptive mechanism, and so the on-line computing burden is reduced. In addition, the proposed control scheme is a smooth control with no chattering phenomena. A simulation example was proposed to demonstrate the effectiveness of the proposed control algorithm. * Supported by National Natural Science Foundation of China (Grant Nos. 60325311, 6053010, 60521003) and Program for Changjiang Scholars and Innovative Research Team in University (Grant No. IRT...

A robustness analysis of discrete-time direct model reference adaptive control

For a class of discrete-time systems with multiplicative uncertainties, the design and analysis of robust direct model reference adaptive control (MRAC) with normalized adaptive law are investigated. By reproving the discrete-time conclusions on the an relationship properties between the input and the output, and the swapping Lemmas I and II, establishing the properties of discrete-time adaptive law, defining the normalizing signal, and relating the signal with all the signals in the closed-loop system, the stability and robustness properties of the discrete-time MRAC scheme are analysed rigorously in a systematic fashion as in the continuous-time case.

Robust direct model reference adaptive control using KP = LDU factorization for multivariable plants

Motivated by the idea of high frequency gain matrix KP = LDU factorization, the purpose of this paper is to study the problem of robust direct model reference adaptive control for more general multivariable plants with unmodeled dynamics and disturbances. For multivariable plants, by reproving some properties similar to those in robust adaptive control theory for SISO plants and redefining the normalizing signal, the relationship between all the signals in the closed-loop plant and the normalizing signal can be established, and the stability and robustness of the closed-loop plant are analyzed rigorously from a qualitative point of view.

Robust direct adaptive control for MIMO systems using Q-parameterization

This paper presents the design of a robust direct adaptive control (DMRAC) algorithm for MIMO systems with focus on the satisfaction of an almost strictly positive real (ASPR) condition in the presence of plant unmodeled dynamics. These unmodeled dynamics are represented as either additive or multiplicative norm bounded perturbations in the transfer function. Design conditions for a feedforward compensator have been developed utilizing the so-called Q parameterization. Illustrative example is presented to validate the algorithm’s use and applicability to control systems with unmodeled dynamics.