Unstructured Uncertainties Research Articles

A particle swarm optimization approach for fuzzy sliding mode control for tracking the robot manipulator

In this paper, an optimal fuzzy sliding mode controller is used for tracking the position of robot manipulator, is presented. In the proposed control, initially by using inverse dynamic method, the known sections of a robot manipulator’s dynamic are eliminated. This elimination is done due to reduction over structured and unstructured uncertainties boundaries. In order to overcome against existing uncertainties for the tracking position of a robot manipulator, a classic sliding mode control is designed. The mathematical proof shows the closed-loop system in the presence of this controller has the global asymptotic stability. Then, by applying the rules that are obtained from the design of classic sliding mode control and TS fuzzy model, a fuzzy sliding mode control is designed that is free of undesirable phenomena of chattering. Eventually, by applying the PSO optimization algorithm, the existing membership functions are adjusted in the way that the error tracking robot manipulator position is converged toward zero. In order to illustrate the performance of the proposed controller, a two degree-of-freedom robot manipulator is used as the case study. The simulation results confirm desirable performance of optimal fuzzy sliding mode control.

A Robust Adaptive Path-Following Controller for a Robotic Wheelchair

This article proposes a path-following controller for robotic wheelchairs (RW) used to transport people suffering of severe muscular diseases, taking into account velocity bounds and dynamic effects. A parameterized dynamic model, which considers the person on board the RW, is used. The model parameters normally change, generating structured uncertainties. Moreover, the dynamic model is proposed under some simplifications, introducing unstructured uncertainties. Finally, time-varying dynamics, caused basically by user movements, are also considered. Hence, the dynamic controller proposed is adaptive and robust. Experimental and simulation results show the effectiveness and the good performance of the proposed control system.

Least-Squares Model-Reference Adaptive Control with Chebyshev Orthogonal Polynomial Approximation

This paper presents a model-reference adaptive control approach for systems with unstructured uncertainty based on two least-squares parameter estimation methods: gradient-based method and recursive least-squares method. The unstructured uncertainty is approximated by Chebyshev orthogonal polynomial basis functions. The use of orthogonal basis functions improves the function approximation significantly and enables better convergence of parameter estimates. The least-squares gradient adaptive control achieves superior parameter convergence as compared to the standard model-reference adaptive control. Flight control simulations were conducted with four adaptive controllers: least-squares gradient adaptive control, recursive least-squares adaptive control, standard model-reference adaptive control, and neural-network adaptive control. The results show that the recursive least-squares adaptive control achieves better robustness as measured by a time-delay margin, while the least-squares gradient adaptive control achieves better tracking performance than both the standard model-reference adaptive control and neural-network adaptive control.

Controllability robustness of linear interval systems with delay in control and unstructured uncertainties

The controllability robustness problem for the linear interval systems with both delay in control and unstructured uncertainties is studied in this paper. The rank preservation problem is converted to the non-singularity analysis problem of the minors of the matrix in discussion. Based on some essential properties of matrix measures, a new, sufficient, algebraically elegant criterion for the robust controllability of linear interval systems with both delay in control and unstructured uncertainties is established. A numerical example is given to illustrate the application of the proposed sufficient algebraic criterion.

Computationally Efficient Adaptive Type-2 Fuzzy Control of Flexible-Joint Manipulators

In this paper, we introduce an adaptive type-2 fuzzy logic controller (FLC) for flexible-joint manipulators with structured and unstructured dynamical uncertainties. Simplified interval fuzzy sets are used for real-time efficiency, and internal stability is enhanced by adopting a trade-off strategy between the manipulator’s and the actuators’ velocities. Furthermore, the control scheme is independent of the computationally expensive noisy torque and acceleration signals. The controller is validated through a set of numerical simulations and by comparing it against its type-1 counterpart. The ability of the adaptive type-2 FLC in coping with large magnitudes of uncertainties yields an improved performance. The stability of the proposed control system is guaranteed using Lyapunov stability theory.

Anti-windup and the preservation of robustness against structured norm-bounded uncertainty

SUMMARY Anti-windup systems are modified control structures, which are designed to compensate against the detrimental effects of saturations. This manuscript considers primarily the stability robustness of two well-known anti-windup structures. Sufficient conditions for the stability robustness of the anti-windup structures and optimal robustness against structured norm-bounded plant uncertainty are found. A saturated loop is said to be optimally robust if the constrained loop is as robust as its unconstrained counterpart. The robustness condition is shown to be less conservative than existing results on additive uncertainty. Although it is known that the conventional internal model control provides optimal robustness against additive unstructured uncertainty, this is not the case against the more general uncertainty structure. Copyright © 2013 John Wiley & Sons, Ltd.

Evaluation Performance of IC Engine: Linear Tunable Gain Computed Torque Controller vs. Sliding Mode Controller

Design a nonlinear controller for second order nonlinear uncertain dynamical systems (e.g., internal combustion engine) is one of the most important challenging works. This paper focuses on the comparative study between two important nonlinear controllers namely; computed torque controller (CTC) and sliding mode controller (SMC) and applied to internal combustion (IC) engine in presence of uncertainties. In order to provide high performance nonlinear methodology, sliding mode controller and computed torque controller are selected. Pure SMC and CTC can be used to control of partly known nonlinear dynamic parameters of IC engine. Pure sliding mode controller and computed torque controller have difficulty in handling unstructured model uncertainties. To solve this problem applied linear error-based tuning method to sliding mode controller and computed torque controller for adjusting the sliding surface gain ( ) and linear inner loop gain ( ). Since the sliding surface gain ( ) and linear inner loop gain ( ) are adjusted by linear error-based tuning method. In this research new and new are obtained by the previous and multiple gains updating factor . The results demonstrate that the error-based linear SMC and CTC are model-based controllers which works well in certain and uncertain system. These controllers have acceptable performance in presence of uncertainty.

A Combined Backstepping and Stochastic Small-Gain Approach to Robust Adaptive Fuzzy Output Feedback Control

In this paper, an adaptive fuzzy output feedback control approach is investigated for a class of stochastic nonlinear strict-feedback systems without the requirement of states measurement. The stochastic nonlinear system addressed in this paper is assumed to possess unstructured uncertainties (unknown nonlinear functions) and, in the presence of unmodeled dynamics, dynamics disturbances. Fuzzy logic systems are used to approximate the unstructured uncertainties, and a fuzzy state observer is designed to estimate the unmeasured states. By combining the backstepping design technique with the stochastic small-gain approach, a new adaptive fuzzy output feedback control approach is developed. It is proved that the proposed control approach can guarantee that the closed-loop system is input-state-practically stability (ISpS) in probability, and the observer errors and the output of the system converge to a small neighborhood of the origin by appropriate choice of the design parameters. Simulation results are included to indicate that the proposed adaptive fuzzy control approach has a satisfactory control performance. In addition, the simulation comparisons with the previous methods show that the proposed adaptive fuzzy control approach has robustness to the dynamical uncertainties.

Adaptive fuzzy sliding mode control of a chaotic pendulum with noisy signals

AbstractChaotic response is related to a dense set of unstable periodic orbits (UPOs) and the system often visits the neighborhood of each one of them. Moreover, chaos has sensitive dependence to initial conditions, which implies that the system evolution may be altered by small perturbations. Chaos control is based on the richness of chaotic behavior and may be understood as the use of tiny perturbations for the stabilization of an UPO enclosed in a chaotic attractor. It makes this kind of behavior to be desirable in a variety of applications, since one of these UPOs can provide better performance than others in a particular situation. In this work, an adaptive fuzzy sliding mode controller is combined with the close return method for the stabilization of UPOs in a chaotic pendulum. The adaptive fuzzy inference system is embedded in a smooth sliding mode controller to cope with both structured and unstructured uncertainties. Since noise contamination is unavoidable in experimental data acquisition, this work also investigates the effect of noisy signals on the used control law, verifying their influence on the system stabilization and on the required control action. Numerical results are presented in order to illustrate the ability of the proposed control scheme to track UPOs even in the presence of modeling inaccuracies and noisy input signals.

Adaptive fuzzy control of uncertain stochastic nonlinear systems with unknown dead zone using small-gain approach

This paper considers the adaptive fuzzy robust control problem for a class of single-input and single-output (SISO) stochastic nonlinear systems in strict-feedback form. The systems under study possess unstructured uncertainties, unknown dead-zone, uncertain dynamics and unknown gain functions. In the controller design, fuzzy logic systems are adopted to approximate the unknown functions, and the uncertain nonlinear system is therefore transformed into an uncertain parameterized system with unmodeled dynamics. By combining the backstepping technique with the stochastic small-gain approach, a novel adaptive fuzzy robust control scheme is developed. It is shown that the proposed control approach can guarantee that the closed-loop system is input-state-practically stable (ISpS) in probability, and the output of the system converges to a small neighborhood of the origin by appropriately tuning several design parameters. Simulation results are provided to illustrate the effectiveness of the proposed control approach.

Robust Active Vibration Control of Smart Structures; a Comparison between Two Approaches: µ-Synthesis & LMI-Based Design

The purpose of this paper is comparing the performance of two robust control designing approaches in smart structures. First, an accurate model of a homogeneous plate with special boundary conditions is derived by using of modal analysis. Then, some primitive p late's modes are considered as nominal system and the remaining modes are left as a mu ltip licat ive unstructured modelling uncertainty. Next, t wo robust controller are designed using µ-Synthesis & LMI-Based Design approaches based on the augmented plant composed of the nominal model and its accompanied uncertainty. Finally, the robustness of two uncertain closed-loop models and the d ifference between t wo controller performances has been investigated. Obtained results show the higher performance of LMI-Based Design approach in rejection of random disturbances.

Controllability Robustness of Linear Interval Systems with/without State Delay and with Unstructured Parametric Uncertainties

The robust controllability problem for the linear interval systems with/without state delay and with unstructured parametric uncertainties is studied in this paper. The rank preservation problem is converted to the nonsingularity analysis problem of the minors of the matrix under discussion. Based on some essential properties of matrix measures, two new sufficient algebraically elegant criteria for the robust controllability of linear interval systems with/without state delay and with unstructured parametric uncertainties are established. Two numerical examples are given to illustrate the applications of the proposed sufficient algebraic criteria, where one example is also presented to show that the proposed sufficient condition for the linear interval systems having no state delay and no unstructured parametric uncertainties can obtain less conservative results than the existing ones reported recently in the literature.

Adaptive Robust Motion Control of Direct-Drive DC Motors with Continuous Friction Compensation

Uncertainties including the structured and unstructured, especially the nonlinear frictions, always exist in physical servo systems and degrade their tracking accuracy. In this paper, a practical method named adaptive robust controller (ARC) is synthesized with a continuous differentiable friction model for high accuracy motion control of a direct-drive dc motor, which results in a continuous control input and thus is more suitable for application. To further reduce the noise sensitivity and improve the tracking accuracy, a desired compensation version of the proposed adaptive robust controller is also developed and its stability is guaranteed by a proper robust law. The proposed controllers not only account for the structured uncertainties (e.g., parametric uncertainties) but also for the unstructured uncertainties (e.g., unconsidered nonlinear frictions). Furthermore, the controllers theoretically guarantee a prescribed output tracking transient performance and final tracking accuracy in both structured and unstructured uncertainties while achieving asymptotic output tracking in the absence of unstructured uncertainties, which is very important for high accuracy control of motion systems. Extensive comparative experimental results are obtained to verify the high-performance nature of the proposed control strategies.

Design and Development of a ?-Synthesis Controller for a Flexible Robotic Manipulator, Modelled as a Rotating Euler-Bernoulli Beam

In this paper, a robust control strategy for a robotic manipulator, modelled as a cantilever rotating Euler-Bernoulli beam, is developed. Imprecision in the payload mass, unknown properties of the manipulator link, and torque disturbance are included as the sources of uncertainty. The objective is to achieve a desired angular rotation while the vibration of the manipulator tip is suppressed and the control system remains in a stable region. The control input of the system is an external driving torque. For formulation of the continuous system, the mode summation technique is used and equations of motion are described in the Laplace domain. Then, unstructured uncertainties are included in the form of multiplicative input uncertainty. The μ-synthesis control approach is used and an H∞ optimal robust controller is developed based on the DK-iteration algorithm. Results show that the designed controller guarantees the robust stability and performance of the perturbed system against existing uncertainties. Consequently, stability of the closed-loop system, disturbance rejection, and trajectory tracking performance are achieved.

Swarm optimization tuned fuzzy sliding mode control design for a class of nonlinear systems in presence of uncertainties

This paper provides an optimal controlling approach for a class of nonlinear systems with structured and unstructured uncertainties using fuzzy sliding mode control. First known dynamics of the system are eliminated through feedback linearization and then optimal fuzzy sliding mode controller is designed using an intelligent fuzzy controller based on Sugeno-Type structure. The proposed controller is optimized by a novel heuristic algorithm namely Particle Swarm Optimization with random inertia Weight RNW-PSO. In order to handle, the uncertainties Lyapunov method is used. There are no signs of the undesired chattering phenomenon in the proposed method. The globally asymptotic stability of the closed-loop system is mathematically proved. Finally, this control method is applied to the inverted pendulum system as a case study. Simulation results show desirability of the system performance.

Robust control stability using the error loop

This paper formulates the error loop as a tool for designing robust stability control systems in the presence of structured and unstructured uncertainties. The error loop indicates that uncertainties can be accommodated through the design of the noise estimator, which is the unique feedback channel from plant to control. The real-time model that is embedded in the control unit and the noise estimator constitute a state predictor. The embedded model consists of a controllable dynamics plus a disturbance dynamics fed by the noise estimator. It is shown that causality constraint prevents perfect cancellation of causal uncertainties (unknown disturbance), but makes the control law which is fed by the state predictor to play a role, thus offering a further degree of freedom. Employing asymptotic expansions of the closed-loop transfer functions, simple, explicit design formulae derive from stability inequalities. They relate closed-loop eigenvalues to model parameters and requirements, and define an admissible frequency band for the state predictor bandwidth. This paper restricts formulation to the univariate case. A simple example is provided with simulated and experimental data.

Design of the Microsatellite Attitude Control System Using the Mixed Method via LMI Optimization

Due to the space missions limited budget, small satellite cluster or constellation would be an economical choice. From risk-sharing viewpoint, a number of smaller satellites have a significant reliability advantage over a bigger one. Generally, one satellite is subject to two types of uncertainties: structured uncertainty that represents some satellite parameter variation and the unstructured uncertainty that represents some kind of the satellite model error. On the other hand, the Satellite Attitude Control (SAC) design becomes more vulnerable to uncertainty disturbances like model error and moment-of-inertia variation as the satellite has great decrease in size and weight. This is the case for a microsatellite with mass less than 100 kg where the ACS performance and robustness become very sensitive to both kinds of uncertainties. As a result, the design of the SAC has to deal with both types of uncertainties which is associated with the drawback between controller performance and robustness. The purpose of this work is to model a microsatellite taking into account the uncertainties and to perform the Control System Design based on the mixed methodology via LMI optimization.

Controller Design of Electric Loading System based on T-S Fuzzy Logic

Electric loading system (ELS) simulates aerodynamic load and exerts the load on actuation system. The key issue of ELS is how to eliminate the influence of extra torque caused by actuation system. In order to overcome these difficulties, we propose an adaptive fuzzy torque control (AFTC) algorithm. Takagi-Sugeno fuzzy logic system is utilized to compensate parametric uncertainties and unstructured uncertainties. The output velocity of actuator identified model is introduced into AFTC aiming to eliminate extra torque. The closed-loop stability is studied and the control system is proved to be semi-globally uniformly ultimately bounded. The proposed AFTC algorithm is applied to an ELS and the comparative experimental results indicate that AFTC controller is effective for ELS to achieve a guaranteed transient as well as final tracking accuracy.

Robust Control Methods a Systematic Survey

The paper addresses the problem how to recognize a level of robust controller design and is aimed show the difficulties of implementation for practical use. In the first part of paper we introduce the survey of robust controller design for SISO systems with generalization design procedure for structured and unstructured uncertainties. The second part of paper is devoted to MIMO systems. In the frequency domain robust controller design procedure we reduce to independent design of SISO subsystems and in time domain the LMI or BMI approaches with polytopic system description are favorable.

Embedding of Uncertainty Propagation: Application to Hierarchical Performance Analysis

The article proposes an approach to embed the propagation of structured uncertainty through a system in a system with one unstructured uncertainty. This embedding is interesting as it allows to use the classical analysis and design tools such H∞ design and μ-analysis or synthesis. A strong motivation is to improve the computational efficiency of the analysis for large-scale uncertain systems using a hierarchical approach. Examples are provided for both the embedding in the SISO and MIMO cases and for the hierarchical performance analysis of an uncertain Phase-Locked-Loop network.