Robust Control Synthesis Research Articles

IDENTIFICATION OF THE MATHEMATICAL MODELS OF THE TECHNOLOGICAL OBJECTS FOR ROBUST CONTROL SYSTEMS

Context. The problem of identification of the mathematical models of the technological objects on the basis of which the robust control system is subsequently synthesized has been considered. The methods of identification of the mathematical models of the technological objects for robust control are the target of the research. Objective. The purpose of the research is to develop recommendations for the existing methods of identifying the mathematical models of the technological objects for robust control to allow the effective application of the robust control systems as well as to increase the energy efficiency of the system as a whole. Method. The suggested recommendations for the identification of the mathematical models of the technological objects aimed at the further synthesis of robust control are divided into two types – with a known and an unknown area of uncertainty. For the former with the mathematical model which is identified only in the nominal mode the existing methods for identifying the continuous models in accordance with the experimentally obtained data are preferable. Taking the multidimensionality and multiplicity of most technological objects into account, the structure of the model in the space of time variables is recommended. It has been suggested to reduce the area of uncertainty to the additive or multiplicative form for the identification of the mathematical models for which, in addition to the nominal model, identification of the area of uncertainty is stipulated. In this case, several models in different operating object modes are used, while the uncertainty is calculated as the distance between the nominal and other models on the frequency grid with the further approximation of the filters of the preassigned order. Results. The suggested algorithm for identifying the mathematical models with the area of uncertainty has been implemented and investigated for a production object – the subsystem of the levels of the diagonal extraction plant of a sugar-mill. Conclusions. The performed experiments have confirmed the efficiency of the proposed calculation of the area of uncertainty of the mathematical models of the technological objects, while the proposed recommendations for the identification of the mathematical models for robust control can be used in practice. Further research is aimed at identifying the area of uncertainty of the closed control systems.

Robust Controller Synthesis for Airborne Electro-Optical Device Line-of-Sight Stabilization System with Saturating Actuators

A technique of multiobjective robust controller synthesis for an electro-optical device line-of-sight stabilization system with saturating actuators is developed on the basis of polytopic linear parameter-varying system theory. From the computational point of view, the synthesis procedure is reduced to convex optimization under constraints expressed in the form of linear matrix inequalities. The multiobjective synthesis of the robust control law for the stabilization system being considered is performed.

Nonlinear robust control of high-speed supercavitating vehicle in the vertical plane

The supercavitating vehicle can quickly become unstable under the influence of the planing force and external disturbances due to waves and currents. The planing force demonstrates nonlinear characteristics which can be described by the vehicle state variables. Strict standards for maneuvering strategy are required for high-speed vehicles to operate, particularly guidance, navigation, and control of underwater maneuver. In reality, the high-speed supercavitating vehicle dynamics present various control issues and challenges. This article proposes the nonlinear robust control synthesis to manipulate the vertical plane of the high-speed supercavitating vehicle against the planing force or parameter variations as well as external disturbances. The control synthesis is implemented by solving an algebraic Riccati equation at each iteration of the control algorithm with the updated system states, which is a so-called state-dependent Riccati equation. The control loops in the dive-plane satisfy an [Formula: see text] performance criterion that can reject external disturbances with perturbations. Simulation results show that the controlled vehicle system guarantees fast transient responses with steady-state performance. Besides, the proposed controller can eliminate up to 62% of disturbances and provides the robust performance against large planing force and parametric uncertainties. This new vehicle technology with active controller offers the potential strategy of higher speed and higher maneuverability solutions for various purposes of underwater maneuvering.

Robust control synthesis for CNC machine spindle

This paper aims to analyze the dynamic stability and build the robust controller for motorized spindle system under parametric variations, external disturbances and measurement noises. A nonlinear model has been established for the machine tool spindles. The phase portrait and bifurcation analyses are provided to show dynamical behaviors for spindle machining. The spindle operations can be dynamically stables or unstable under parameter variations and disturbances. By using the robust control synthesis, the system designers can shape the frequency responses of the desired model which satisfies both transient response and robustness against various uncertainties. In fact, the robust controller can effectively attenuate exogenous disturbances and sensor noises during machining process. Finally, the simulations results demonstrate that the presented controller provides robust stability for the spindle speeds, along with excellent abilities of noise as well as disturbance attenuations.

Consensus for time-delay multi-agent systems with H∞ performance in finite frequency domains

ABSTRACTThis paper considers the problem of robust control synthesis such that time-delay multi-agent systems are consensus and capture the finite frequency domain performance. Using a linear transformation, the consensus problem is first transformed into a partial stability problem. Then, based on a dual version of generalised Kalman–Yakubovich–Popov (GKYP) lemma and a partial multiplier expansion method, new sufficient conditions guaranteeing the existence of static output feedback controller are proposed in terms of linear matrix inequalities (LMIs) without introducing conservatism. Finally, the effectiveness of the presented method is illustrated via a two-cart-one-spring system and a numerical example.

ISS Robust Stabilization of State-Delayed Discrete-Time Systems With Bounded Delay Variation and Saturating Actuators

We address the problem of robust input-to-state stabilization of parameter-varying discrete-time systems with time-varying state delay, saturating actuators, and subject to $\ell _2$ -limited disturbance. It is assumed that the delay belongs to a known interval and its maximum variation between two consecutive instants is taken into account. The proposed convex delay-dependent conditions for the synthesis of robust state feedback controllers ensure local input-to-state stability of the closed-loop system for a set of initial conditions and for energy-bounded disturbance signals. However, the computed controllers do not require the real-time knowledge of the delay. The approach is based on the rewriting of the saturating and delayed system in terms of a switching uncertain augmented delay-free system with a dead-zone nonlinearity and on the application of the generalized sector condition. To illustrate the efficiency of our approach, we compare it by means of numerical examples with others found in the literature.

Robust Non-Fragile Fuzzy Control of Uncertain DC Microgrids Feeding Constant Power Loads

This paper investigates the problem of dynamic stabilization of dc microgrids (MGs) through a robust non-fragile fuzzy control synthesis of power buffer. The suggested robust fuzzy controller is designed to quickly stabilize the MGs by circulating the power between the dc link and an energy storage system (ESS). By employing the exponential stability analysis and Takagi–Sugeno fuzzy modeling, sufficient controller design conditions are derived in terms of linear matrix inequalities, which bring about a simple, systematic, and effective controller. The proposed approach is resilient against the uncertainties of the dc MG and ESS parameters. To show the merits of the proposed approach, it is applied to a dc MG that feeds one constant power load. It is shown that the proposed approach is more robust against system and controller uncertainties compared to the existing results. Finally, experimental results are then presented that show the transient performance improvement of the closed-loop system compared to the state-of-the-art methods.

Robust control synthesis for discrete-time uncertain semi-Markov jump systems

This paper studies the control synthesis for uncertain semi-Markov jump systems in a discrete-time domain subjected to external disturbance. The switching between modes is determined by a function of the transition probability and the sojourn-time distribution between two neighbouring modes. Based on the σ-error mean square stability criterion, time-varying controllers are designed to stabilise the system. By constructing a holding time dependent Lyapunov function, time-varying state-feedback controllers are obtained that meet a set of sufficient conditions in the form of linear matrix inequalities. Two examples, including a DC motor system, are presented to show the validity of the proposed control scheme.

A Method to Robustify Exact Linearization Against Parameter Uncertainty

This paper addresses the issue of uncertain parameters in the case of the control of nonlinear systems which are exact linearizable by state feedback. It is shown that the linearizing feedback may be complemented by an additional robustifying compensator, designed to ensure robust stability and performance against the uncertainty of some model parameters. This allows to bridge two state-of-the-art design methodologies such as exact linearization and robust control synthesis. Exact linearization allows the transformation of nonlinear dynamics into linear ones by an eventually dynamic state feedback and by a change of coordinates. However, due to the uncertain nature of some model parameters, their nominal values used in the transformation may be different from their real values. This parameter misfit implies that the resulting transformed dynamics may still include non-linearities or may be a linear system, but different from the one that results for the nominal parameter values. The paper proposes a procedure to cover the uncertainties remaining after exact linearization and to design an additional linear compensator, denoted by K(s), to ensure robust performance and stability. The design of the compensator K(s) involves standard $$\mathcal{H}_\infty$$ techniques, based on an output multiplicative uncertainty structure. The weighting matrices of the output multiplicative structure are obtained such that they cover a model set obtained by linearizing the transformed nonlinear system over a sufficiently fine grid above the uncertain parameter range. The suggested approach is illustrated by multiple (SISO and MIMO) examples, including a two-degrees-of-freedom robotic arm. It is shown by simulation that the additional robustifying compensator may stabilize the system for parameter values that would result in unstable behavior without its application and may also result in a better tracking performance.

Learning Robust LQ-Controllers Using Application Oriented Exploration

This letter concerns the problem of learning robust LQ-controllers, when the dynamics of the linear system are unknown. First, we propose a robust control synthesis method to minimize the worst-case LQ cost, with probability 1 - δ, given empirical observations of the system. Next, we propose an approximate dual controller that simultaneously regulates the system and reduces model uncertainty. The objective of the dual controller is to minimize the worst-case cost attained by a new robust controller, synthesized with the reduced model uncertainty. The dual controller is subject to an exploration budget in the sense that it has constraints on its worst-case cost with respect to the current model uncertainty. In our numerical experiments, we observe better performance of the proposed robust LQ regulator over the existing methods. Moreover, the dual control strategy gives promising results in comparison with the common greedy random exploration strategies.

ROBUST CONTROLLER FOR SUPERSONIC UNMANNED AERIAL VEHICLE

The article is devoted to the synthesis of robust controllers of supersonic unmanned aerial vehicle motion parameters. During the flight, the velocity and altitude of the aircraft varies rapidly within wide limits. Therefore, the required quality of control on each trajectory is provided by a set of dynamic controllers with constant coefficients. The article substantiates the number of such controllers, researches the range of their efficiency. The obtained restrictions on the amplitude-frequency characteristics and weight functions are given. Transients are shown

Iterative ‐conic controller synthesis

SummaryThis paper proposes a method to synthesize controllers that minimize an upper bound on the closed‐loop ‐norm while imposing desired controller conic bounds. An initial conic controller is synthesized and iteratively improved. Conic sectors can be used to characterize a variety of input‐output properties, such as gain, phase, and minimum gain. If such plant properties hold robustly to uncertainty present, then closed‐loop stability can be ensured robustly via the Conic Sector Theorem by imposing desired controller conic bounds. Consequently, this paper provides a versatile optimal and robust controller synthesis method. Moreover, it relies only on the solution of convex optimization problems subject to linear matrix inequality constraints, making it readily implementable.

Heart Rate Variability as a Prognostic Factor for Cancer Survival - A Systematic Review

This paper addresses the problems of robust stability analysis and L1-gain controller synthesis for uncertain impulsive positive systems. First, by employing the idea of impulse interval partitioning, an impulse-time-dependent discretized copositive Lyapunov function is proposed to analyze the robust stability and L1-gain performance of the considered system without control inputs, and several stability conditions and L1-gain criteria are respectively derived. Subsequently, a sufficient condition is formulated for the existence of state-feedback controllers with which not only the positivity and robust uniform asymptotic stability of the resulting closed-loop system are guaranteed, but also a prescribed L1-gain performance is satisfied simultaneously. Furthermore, to make the controller synthesis problem numerically tractable, we propose an iterative convex optimization algorithm to compute the desired controller parameters. Finally, three numerical examples and two realistic examples are presented to show the effectiveness and applicability of the proposed methodology.

IMPROVING OF ELECTROMECHANICAL STABILIZATION SYSTEMS ACCURACY

Aim. Improving of accuracy parameters and reducing of sensitivity to changes of plant parameters for nonlinear robust tank main armament guidance and stabilization electromechanical systems based on synchronous motor with permanent magnets and vector control. Methodology. The method of multiobjective synthesis of nonlinear robust control by nonlinear tank main armament stabilization electromechanical system taking into account the elastic oscillations of the tank gun barrel as a discrete-continuous plant and with parametric uncertainty based on the multiobjective optimization. The target vector of robust control choice by solving the corresponding multicriterion nonlinear programming problem in which the calculation of the vectors of the objective function and constraints is algorithmic and associated with synthesis of nonlinear robust controllers and modeling of the synthesized system for various modes of operation of the system, with different input signals and for various values of the plant parameters. Synthesis of nonlinear robust controllers and non-linear robust observers reduces to solving the system of Hamilton-Jacobi-Isaacs equations. Results. The results of the synthesis of a nonlinear robust tank main armament guidance and stabilization electromechanical systems are presented. Comparison of the dynamic characteristics of the synthesized tank main armament stabilization electromechanical systems showed that the use of synthesized nonlinear robust controllers allowed to improve the accuracy parameters and reduce the sensitivity of the system to changes of plant parameters in comparison with the existing system. Originality. For the first time carried out the multiobjective synthesis of nonlinear robust tank main armament stabilization electromechanical systems. Practical value. Practical recommendations are given on reasonable choice of the gain matrix for the nonlinear feedbacks of the regulator and the nonlinear observer of the tank main armament stabilization electromechanical systems, which allows improving the dynamic characteristics and reducing the sensitivity of the system to plant parameters changing in comparison with the existing system.

Synthesis of robust controllers for an object with delay using traditional control laws

Synthesis of robust controllers for an object with delay using traditional control laws

Robust stability analysis and controller synthesis for uncertain impulsive positive systems under [formula omitted]-gain performance

This paper addresses the problems of robust stability analysis and L1-gain controller synthesis for uncertain impulsive positive systems. First, by employing the idea of impulse interval partitioning, an impulse-time-dependent discretized copositive Lyapunov function is proposed to analyze the robust stability and L1-gain performance of the considered system without control inputs, and several stability conditions and L1-gain criteria are respectively derived. Subsequently, a sufficient condition is formulated for the existence of state-feedback controllers with which not only the positivity and robust uniform asymptotic stability of the resulting closed-loop system are guaranteed, but also a prescribed L1-gain performance is satisfied simultaneously. Furthermore, to make the controller synthesis problem numerically tractable, we propose an iterative convex optimization algorithm to compute the desired controller parameters. Finally, three numerical examples and two realistic examples are presented to show the effectiveness and applicability of the proposed methodology.

Simultaneous design of AWC and nonlinear controller for uncertain nonlinear systems under input saturation

SummaryThis article addresses a novel technique for the simultaneous design of a robust nonlinear controller and static anti‐windup compensator (AWC) for uncertain nonlinear systems under actuator saturation and exogenous bounded input. The system is presumed to have locally Lipschitz nonlinearities, time‐varying uncertainties (appearing both in the linear as well as nonlinear dynamics and both in the state in addition to the output equations), and external norm‐bounded inputs both in the state and the output equations. Several bilinear matrix inequality–based conditions are derived to simultaneously design the robust nonlinear controller and AWC gains for uncertain nonlinear systems by employing the Lyapunov functional, reformulated Lipschitz property, uncertainty bounds, linear parameter‐varying approach, modified local and global sector conditions, iterative linear matrix inequality algorithm, convex optimization procedure, and gain minimization. The proposed multiobjective AWC‐based dynamic robust nonlinear controller guarantees the mitigation of saturation effects, robustness against time‐varying parametric norm‐bounded uncertainties, the asymptotic stability of the closed‐loop nonlinear system under zero external disturbances, and the attenuation of disturbance effects under nonzero external disturbances. The effectiveness of the proposed AWC‐based dynamic robust nonlinear controller synthesis scheme is illustrated by simulation examples.

Relaxed Robust Stabilization Conditions for Nonhomogeneous Markovian Jump Systems with Actuator Saturation and General Switching Policies

This paper investigates the robust control synthesis problem of nonhomogeneous Markovian jump systems with actuator saturation and uncertainties. First of all, to make a comprehensive mode-transition description, three separate mode sets are established according to the property of transition rates. And then, to improve the numerical solvability of inequality conditions dependent on time-varying transition rates, two useful relaxation methods are developed on the basis of the mode sets. Especially, by taking advantage of a new zero-sum constraint, the relaxation process is further evolved such that the conservatism arising from incomplete knowledge of transition rates can be reduced. Lastly, this paper provides the LMI-based conditions capable of estimating the attraction domain as well as of designing a mode-dependent robust control.

Rendering Stiff Virtual Walls Using Model Matching Based Haptic Controller.

This paper presents a model matching framework for design of haptic controllers. The controller design problem is formulated as a sequence of ${H_{\infty }}$ optimization problems in order to achieve maximal transparency bandwidth. This enables automatic synthesis of robust controllers to achieve a desired bandwidth while limiting actuator forces and guaranteeing stability. This method is applied to address the problem of accurate rendering of high-stiffness virtual walls. Simulation of virtual walls of various stiffnesses are tested on a PHANToM Premium 1.5, at a sampling rate of 1KHz. The sampled nature of the interface, sensor quantization and Coulomb friction impose limits on the maximum stiffness that can be stably achieved with the commonly used open loop impedance controller. Results presented here demonstrate that the proposed controllers can be used to accurately render virtual walls with stiffness up to 5000N/m in an oscillation free manner. This stiffness value is well beyond stability limits for the PHANToM under open loop impedance control. Relationships between the weighting functions and the transparency bandwidth are established to outline a procedure for selection and tuning of the weighting functions. Specifically, it is shown that through appropriate choice of weighting functions high-frequency oscillations observed during rendering of stiff surfaces can be eliminated. The passivity of the designed controllers over the frequency range of operation is verified.

Delay-Dependent Admissibility Analysis and Dissipative Control for T-S Fuzzy Time-Delay Descriptor Systems Subject to Actuator Saturation

In this paper, a delay-dependent admissibility analysis method and dissipative controller design are developed for a class of nonlinear time-delay descriptor systems subject to actuator saturation and L 2 -disturbances via a Takagi-Sugeno (T-S) fuzzy model. A less conservative admissible condition is first derived under which the system is not only regular, impulse free but also stable under certain initial conditions. The method can eliminate the impulsive behavior of a descriptor system so as to ensure the existence and uniqueness of solutions. The estimate of attraction domain is also determined in which the admissible initial states converge asymptotically to the origin. The disturbance attenuation capability is studied by designing the dissipative fuzzy controller such that the closed-loop system is admissible and holds the dissipative performance for the prescribed disturbance attenuation level and L 2 -disturbances. The method is more suitable for admissibility analysis and robust control synthesis. Moreover, H ∞ control processes can be achieved in the same design process, which shows that the cost and time may potentially be reduced when a controller is designed for an actual physical system. Simulations are performed to validate the proposed methods and illustrate the decrease in conservativeness for a classic nonlinear system based on the T-S fuzzy time-delay descriptor model under actuator saturation and L 2 -disturbances. The study seeks to establish a foundation for investigating the control synthesis of T-S fuzzy time-delay descriptor systems subject to actuator saturation.