Robust Control Toolbox In Matlab Research Articles

Comparing the Performance of Robust Controllers for Vibration Suppression in Long Rotor Systems

In this paper, the vibration control of the multivariable model of rotor bearing systems is considered for investigation. Some simply structured controllers that can suppress vibrational disturbances are tested for their robustness via the H∞ optimality criteria. Initially, intelligent optimisation techniques are used to minimize the H∞ mixed-sensitivity norm of the Linear Fractional Transformation (LFT) of the simple two-term PI controllers acting on the rotor system models. This results in some controllers that can suppress the vibration but with a slow oscillatory response. After this, an appropriate interpretation of the Bode plot singular values of the combined sensitivity and control effort matrix is used to explain the performance shortcomings of this controller. Moreover, the existing simply structured controllers in the literature exhibiting a faster performance are examined by using singular value plots. It is shown that when the maximum singular value of the control effort matrix drops below the 0 db line, the performance will be boosted. Finally, the H∞ controllers are designed by using the robust control toolbox in MATLAB. This resulted in rapid disturbance rejection, with the vibration amplitude diminishing to zero after 0.3 s due to double-step disturbances. However, these controllers in the frequency domain have an order of eight and may not be realizable to be implemented in practice. It is concluded that examining the Bode plot of the maximum singular value of the control effort matrix is a useful tool for evaluating performance in the frequency domain. However, designing robust controllers by toolboxes in the time domain can lead to superb performance with higher-order controllers.

Linear Fractional Transformation Modeling of Multibody Dynamics Around Parameter-Dependent Equilibrium

This paper proposes a new Linear Fractional Transformation (LFT) modeling approach for uncertain Linear Parameter Varying (LPV) multibody systems with parameter-dependent equilibrium. Traditional multibody approaches, which consist in building the nonlinear model of the whole structure and linearizing it around equilibrium after a numerical trimming, do not allow to isolate parametric variations with the LFT form. Although additional techniques, such as polynomial fitting or symbolic linearization, can provide an LFT model, they may be time-consuming or miss worst-case configurations. The proposed approach relies on the trimming and linearization of the equations at the substructure level, before assembly of the multibody structure, which allows to only perform operations that preserve the LFT form throughout the linearization process. Since the physical origin of the parameters is retained, the linearized LFT-LPV model of the structure exactly covers all plants, in a single parametric model, without introducing conservatism or fitting errors. An application to the LFT-LPV modeling of a robotic arm is proposed; in its nominal configuration, the model obtained with the proposed approach matches the model provided by the software Simscape Multibody, but it is enhanced with parametric variations with the LFT form; a robust LPV synthesis is performed using Matlab robust control toolbox to illustrate the capacity of the proposed approach for control design.

Robust control for a tracking electromechanical system

<p>A strategy for the design of robust control of tracking electromechanical systems based on 𝐻∞ synthesis is proposed. Proposed methods are based on the operations on frequency characteristics of control systems designed and developed using the MATLAB robust control toolbox. Determination of the singular values for a transfer matrix of the control system reduces the disturbances and guarantees its stability margin. For selecting the weighted transfer functions, the basic recommendations are formulated. The efficiency of the proposed approach is verified by robust control of an elastically coupled two-mass system whose parameter values are adjusted by matching them with the parameters of one of the supplied robots. The simulation results confirm that the proposed strategy of design of robust control of two-mass elastic coupling system using the 𝐻∞ synthesis is very efficient and significantly reduces the perturbation of parameters of the controlled plant.</p>

Fractional Order Robust Controller for Fractional-Order Interval Plants

Fractional order (FO) calculus in modelling and control applications has been increasingly popular in every scientific field due to its versatility and superiority in various instances. Moreover, the models’ parameters present uncertainties, called intervals. However, the main issue of fractional order elements is related to their implementation. Usually, integer order elements are used through different approximation methods to implement such elements. None of the existing methods discuss the introduction of a fractional element in a fixed-structure robust synthesis method. The objects from the MATLAB's Robust Control Toolbox could not be implied in other than well-known arithmetic operations between the parameters of the fixed-structure controllers, while existing approximations use exponential terms. To overcome this shortcoming, this work proposes and offers the algorithm for an approximation method useful in robust controller synthesis, which is validated for several numerical case studies.

IQClab: A new IQC based toolbox for robustness analysis and control design

Abstract In this paper we present our new integral quadratic constraint (IQC) based toolbox, named IQClab. The toolbox is a versatile extension of the MATLAB Robust Control Toolbox and offers a wide range of possibilities for performing robustness analysis and control design for a large class of uncertain and linear parameter varying (LPV) systems. In addition, IQClab consists of an extensive set of auxiliary tools and functions for performing model reduction, implementing control switching schemes, generating performance weighting functions, among others. Not only is the toolbox easy to use, but it also has a modular build and can be applied in combination with different parsers and solvers. This allows developers to seamlessly include new linear matrix inequality (LMI) and IQC based algorithms as well as other extensions. The aim of the present paper is to provide an overview of the toolbox’s capabilities together with some demonstrations and illustrative numerical examples.

Hydraulic Servo System Control Using Differential Evolution Based Robust Structure Specified H∞ Controller

Synthesis of an H∞ controller usually produces a very high order of controller, and one which is much higher than the plant, causing difficulty in implementing the controller in practical applications, especially those using small microcontrollers. However, systems are always subject to disturbances and un-modeled dynamics. This research introduces modeling and simulations of lower order structures, specifically an H∞ robust controller, to control a hydraulic servo system. A low order controller shortens the gap between the complicated H∞ controllers to the practical embedded control system application. Simulation results show that the proposed controller gives satisfactory results with small settling times and no steady state error. The resulting controller also produced better responses than that of a full order H∞ controller generated using the Matlab Robust Control Toolbox.

ROBUST CONTROL OF LASER ACTUATOR FOR TECHNICAL VISION SYSTEM

Context. The SLAM problem solving for an autonomous mobile robot requires efficient technical means for surrounding terrain scanning with the purpose of its mapping and obstacles detecting. As such means, laser scanning systems are widely used both independently and in combination with other tools as a part of a uniform technical vision system of a mobile robot. One of the problems with a technical vision systems operation is the ability to detect relatively small obstacles, which requires scanning of a limited sector within the field of view or even focusing on a specific point of space. This study is devoted to the issue of improving the reliability of obstacles detecting within the robot field of view by improving the laser actuator of the technical vision system. Objective. The objective of the work is to the reliability increasing of obstacles detection within the robot technical vision system field of view due to the robust control of the actuators of the positioning system of the laser. Method. The classical PD-controller for the laser positioning actuator, which meets the requirements for the quality of the transient process, has been synthesized. The evaluation of robust properties of the obtained control system showed both a significant dependence of the actuator dynamic properties on the variation of the values of the actuator model parameters and the potential possibility of its time response increasing. With the help of the MATLAB Robust Control Toolbox, the controller gains have been redefined to ensure the robust properties of the control system. The analysis of the influence of parametric uncertainties of the actuator model on the system dynamic properties is conducted. Results. A robust PD-controller for the laser beam positioning system actuator for the technical vision system has been synthesized. It combines the simplicity of the implementation of a classic controller with a weak sensitivity to the uncertainties presence. Conclusions. The using of the controller at the mobile robot laser technical vision system will increase the reliability of obstacle detection and, as a result, the accuracy of mapping of a limited sector within the robot field of view under the conditions of the parametric uncertainty of the actuator model.

Simple Adaptive Delta Operator Aircraft Flight Control for Accommodation of Loss of Control Effectiveness

A new proof for stability of delta operator simple adaptive control is presented in terms of a set of Linear Matrix Inequalities (LMIs). The paper shows how to design a feedforward gain to satisfy the LMIs over a polytope of loss of control effectiveness failures. The MATLAB Robust Control Toolbox is used to find the feedforward gain with the smallest norm that satisfies the LMIs. Examples are presented of the F/A-18 aircraft and the Innovative Control Effectors (ICE) tailless aircraft that show the design of a feedforward gain for a loss of control effectiveness in any one control effector. The designs use a fixed eigenstructure assignment controller for an inner loop augmented with the simple adaptive controller. Simulations of both aircraft include simultaneous loss of control effectiveness failure and lateral wind gust. Simulation results for the F/A-18 aircraft show that the adaptive controller achieves almost perfect tracking whereas the nonadaptive controller cannot achieve a coordinated turn when an aileron failure occurs. The ICE tailless aircraft uses sideslip, washed-out stability axis yaw rate, and stability axis roll rate feedback for both the inner loop eigenstructure assignment controller and the simple adaptive controller. However, the adaptive controller also uses bank angle feedback. Simulation results for the ICE tailless aircraft show that the adaptive controller achieves almost perfect tracking whereas the nonadaptive controller diverges when an all moving tip failure occurs.

Synchronization of fuzzy bidirectional associative memory neural networks with various time delays

The problem of synchronization for fuzzy bidirectional associative memory (BAM) neural networks (NNs) with various time delays is formulated and investigated. The various delays consist of discrete delays, unbounded distributed delays and constant delay in the leakage term (i.e. ‘leakage delay’) are considered. Then, some sufficient conditions are presented to guarantee the global asymptotic stability of the error dynamical system by using Lyapunov–Krasovskii functional and linear matrix inequality (LMI) method. As a result, we achieved synchronization of master-slave (drive-response) fuzzy BAM NNs systems. Even, if there is no leakage delay, the obtained results are less restrictive to some known sufficient conditions. Moreover, the proposed results do not require the boundedness, differentiability and monotonicity of the activation functions, which can also be easily checked via the LMI solver in robust control toolbox in Matlab. Furthermore, using a parameter-dependent Lyapunov function approach the synchronization problem for polytopic uncertain fuzzy BAM NNs with various time delays is considered. The parameter uncertainties under consideration are assumed to belong to a fixed convex polytope. Finally, two numerical examples and simulations are given to illustrate the effectiveness of the derived theoretical results.

Computation of the Structured Singular Value via Moment LMI Relaxations

The Structured Singular Value (SSV) provides a powerful tool to test robust stability and performance of feedback systems subject to structured uncertainties. Unfortunately, computing the SSV is an NP-hard problem, and the polynomial-time algorithms available in the literature are only able to provide, except for some special cases, upper and lower bounds on the exact value of the SSV. In this work, we present a new algorithm to compute an upper bound on the SSV in case of mixed real/complex uncertainties. The underlying idea of the developed approach is to formulate the SSV computation as a (nonconvex) polynomial optimization problem, which is relaxed into a sequence of convex optimization problems through moment-based relaxation techniques. Two heuristics to compute a lower bound on the SSV are also discussed. The analyzed numerical examples show that the developed approach provides tighter bounds than the ones computed by the algorithms implemented in the Robust Control Toolbox in Matlab, and it provides, in most of the cases, coincident lower and upper bounds on the structured singular value.

Enhanced Linear Fractional Transformation: a Matlab Toolbox for Space System Modeling and Controller Analysis and Synthesis

Through an example of orbital rendezvous between a flexible spacecraft and a rigid target, this paper presents the Enhanced Linear Fractional Transformation Toolbox (ELFTT) developed under ESA contract in order to support advanced design, validation and verification processes of space system control loop. ELFTT will be distributed within the ESA Member States under an Open Source-like license. It is built on (and fully compatible with) Matlab Robust Control Toolbox RCT. It is dedicated to build, verify, manage Linear Fractional Transformations LFT specialized for space applications. On the one hand, it contains a library of generic LFT models relevant for space applications including typical uncertain actuators models (reaction wheels, thrusters.) uncertain dynamics models (flexible spacecraft, rendezvous dynamics.), uncertain sensors models (star trackers, gyrometer. ), etc. On the other hand, it implements new Matlab functions dedicated to manage the LFT models and to support robust controller synthesis and analysis.

RobustH∞observer‐based tracking control of stochastic immune systems under environmental disturbances and measurement noises

AbstractA robust H∞observer‐based tracking control of stochastic immune response is proposed for therapeutic enhancement to track a prescribed immune response under uncertain initial states, environmental disturbances and measurement noises. The statistics of initial condition, environmental and measurement noises are assumed unavailable. Further, the state variables may not all be available and may be corrupted by measurement noises. Therefore, an observer‐based control design is proposed for robust H∞observer‐based tracking control of stochastic immune systems. The robust H∞control is designed to track a prescribed immune model response in spite of environmental disturbances, uncertain initial conditions and measurement noises. Since the stochastic immune system is highly nonlinear, it is not easy to solve the robust H∞observer‐based tracking control problem directly. A fuzzy model is proposed to interpolate several linearized stochastic immune systems to approximate the nonlinear stochastic immune system via smooth fuzzy membership functions. By the fuzzy approximation method, the H ∞ observer‐based tracking control problem of stochastic immune systems could be easily solved via the linear matrix inequality (LMI) technique with the help of Robust Control Toolbox in Matlab. Finally, anin silicoexample is given to illustrate the design procedure and to confirm the efficiency of the proposed method.Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society

Robust Observer-Based Tracking Control of Hodgkin-Huxley Neuron Systems Under Environmental Disturbances

A nervous system consists of a large number of highly interconnected nerve cells. Nerve cells communicate by generation and transmission of short electrical pulses (action potential). In addition, membrane voltage is the only measurable state in nervous systems. A robust observer-based model reference tracking control is proposed for Hodgkin-Huxley (HH) neuron systems to generate a desired reference response in spite of environmental noises, uncertain initial values, and diffusion currents from other interconnected nerve cells. In order to simplify the robust tracking control design of nonlinear stochastic HH neuron systems, a fuzzy interpolation method is employed to interpolate several linear stochastic systems to approximate a nonlinear stochastic HH neuron system so that the nonlinear robust tracking control problem can be solved by the linear matrix inequality (LMI) technique with the help of Robust Control Toolbox in Matlab. The proposed robust observer-based tracking control scheme can provide new methods for desired action potential generation, suppression of oscillations, and blockage of action potential transmission under environmental noise and diffusion currents. These new methods are useful for patients with different neuron system dysfunctions. Finally, three simulation examples of tracking control of nervous systems are given to illustrate the design procedure and confirm the tracking performance of the proposed method.

Robust synthetic biology design: stochastic game theory approach.

Motivation: Synthetic biology is to engineer artificial biological systems to investigate natural biological phenomena and for a variety of applications. However, the development of synthetic gene networks is still difficult and most newly created gene networks are non-functioning due to uncertain initial conditions and disturbances of extra-cellular environments on the host cell. At present, how to design a robust synthetic gene network to work properly under these uncertain factors is the most important topic of synthetic biology.Results: A robust regulation design is proposed for a stochastic synthetic gene network to achieve the prescribed steady states under these uncertain factors from the minimax regulation perspective. This minimax regulation design problem can be transformed to an equivalent stochastic game problem. Since it is not easy to solve the robust regulation design problem of synthetic gene networks by non-linear stochastic game method directly, the Takagi–Sugeno (T–S) fuzzy model is proposed to approximate the non-linear synthetic gene network via the linear matrix inequality (LMI) technique through the Robust Control Toolbox in Matlab. Finally, an in silico example is given to illustrate the design procedure and to confirm the efficiency and efficacy of the proposed robust gene design method.Availability: http://www.ee.nthu.edu.tw/bschen/SyntheticBioDesign_supplement.pdfContact: bschen@ee.nthu.edu.twSupplementary information: Supplementary data are available at Bioinformatics online.

Robust model matching control of immune systems under environmental disturbances: Dynamic game approach

A robust model matching control of immune response is proposed for therapeutic enhancement to match a prescribed immune response under uncertain initial states and environmental disturbances, including continuous intrusion of exogenous pathogens. The worst-case effect of all possible environmental disturbances and uncertain initial states on the matching for a desired immune response is minimized for the enhanced immune system, i.e. a robust control is designed to track a prescribed immune model response from the minimax matching perspective. This minimax matching problem could herein be transformed to an equivalent dynamic game problem. The exogenous pathogens and environmental disturbances are considered as a player to maximize (worsen) the matching error when the therapeutic control agents are considered as another player to minimize the matching error. Since the innate immune system is highly nonlinear, it is not easy to solve the robust model matching control problem by the nonlinear dynamic game method directly. A fuzzy model is proposed to interpolate several linearized immune systems at different operating points to approximate the innate immune system via smooth fuzzy membership functions. With the help of fuzzy approximation method, the minimax matching control problem of immune systems could be easily solved by the proposed fuzzy dynamic game method via the linear matrix inequality (LMI) technique with the help of Robust Control Toolbox in Matlab. Finally, in silico examples are given to illustrate the design procedure and to confirm the efficiency and efficacy of the proposed method.

Robust Track-Keeping Autopilots for Ships

Design of a track-keeping autopilot for ships using H∞ control theory with the aid of MATLAB robust control toolbox is discussed in this paper. The weighted mixed sensitivity problem is involved when the course-keeping and course-changing controllers are designed. Laboratory simulations have been carried out, the robustness of the designed autopilot is demonstrated by the satisfactory performance under various sea states and different ship speed and loading conditions in the simulations.