Robust Control Synthesis Research Articles

Positive real control for discrete-time singular systems with affine parameter dependence

This paper presents a less conservative and numerically tractable solution to the static state feedback positive real control problem for affinely parameter dependent discrete-time singular systems. Relied on the use of auxiliary matrices and a positive scalar decision variable, a novel necessary and sufficient condition of positive realness is first derived in terms of a strict matrix inequality for linear time-invariant discrete-time singular systems. This characterization leads to a numerically efficient and reliable way for the controller design synthesis. Then, the results are further expanded to parameter dependent singular systems whose coefficient matrices are affine functions of a time-invariant uncertain parameter vector. Both robust analysis and robust controller synthesis are addressed. Numerical examples are included to illustrate the effectiveness of the present results.

Robust control of decomposable LPV systems

This paper considers distributed control of a class of interconnected systems, namely decomposable linear parameter-varying (LPV) systems, which include multi-agent systems with LPV agent models and switching communication topology as a special case. Sufficient conditions for stability are established for uncertain time-invariant as well as for time-varying interconnection topologies in a known set. Recent work on distributed state feedback controller synthesis is extended to robust output feedback controller synthesis. Here robustness refers to variations in the topology as well as the LPV dynamics of the subsystems.

Semi-active sliding mode control of vehicle suspension with magneto-rheological damper

The vehicle semi-active suspension with magneto-rheological damper(MRD) has been a hot topic since this decade, in which the robust control synthesis considering load variation is a challenging task. In this paper, a new semi-active controller based upon the inverse model and sliding mode control (SMC) strategies is proposed for the quarter-vehicle suspension with the magneto-rheological (MR) damper, wherein an ideal skyhook suspension is employed as the control reference model and the vehicle sprung mass is considered as an uncertain parameter. According to the asymptotical stability of SMC, the dynamic errors between the plant and reference systems are used to derive the control damping force acquired by the MR quarter-vehicle suspension system. The proposed modified Bouc-wen hysteretic force-velocity (F-v) model and its inverse model of MR damper, as well as the proposed continuous modulation (CM) filtering algorithm without phase shift are employed to convert the control damping force into the direct drive current of the MR damper. Moreover, the proposed semi-active sliding mode controller (SSMC)-based MR quarter-vehicle suspension is systematically evaluated through comparing the time and frequency domain responses of the sprung and unsprung mass displacement accelerations, suspension travel and the tire dynamic force with those of the passive quarter-vehicle suspension, under three kinds of varied amplitude harmonic, rounded pulse and real-road measured random excitations. The evaluation results illustrate that the proposed SSMC can greatly suppress the vehicle suspension vibration due to uncertainty of the load, and thus improve the ride comfort and handling safety. The study establishes a solid theoretical foundation as the universal control scheme for the adaptive semi-active control of the MR full-vehicle suspension decoupled into four MR quarter-vehicle sub-suspension systems.

A synthesis framework for robust gain-scheduling controllers

We present a general framework for the systematic synthesis of robust gain-scheduling controllers by convex optimization techniques and for uncertain dynamical systems described by standard linear fractional representations. We distinguish between linear time-varying parameters, which are assumed to be available online as scheduling parameters for the controller, and genuine uncertainties, not necessarily time-varying, parametric or linear, that are not available online. Under the rough hypothesis that the control channel is not affected by the unmeasurable uncertainties and that the properties of the uncertainties and scheduling variables are captured by suitable families of integral quadratic constraints, this paper reveals how controller synthesis can be turned into a genuine semi-definite program. The design framework is shown to encompass a rich class of concrete scenarios.

Robust Control of Weight Compensation of the Sections of Spascraft on the Weightlessness Simulation Bench

The structure of the robust stabilization system of cable tension for the test bench of weightlessness simulation was developed. The algorithm of a parametric synthesis of the robust PI controller based on the coefficient method and the criterion of maximum degree of stability was suggested. The operability of the synthesized robust system was confirmed by the results of digital simulation.

ROBUST DISTURBANCES REJECTION IN PUMPING STATIONS CONTROL FOR CENTRALIZED DRINKING WATER DISTRIBUTION SYSTEM

An approach to solving the problem of stabilizing robust water inventory control synthesis for drinking water distribution system of a large city is proposed. The mathematical model of drinking water distribution system is presented in the form of a nonlinear discrete state-space model with time-delay. The technique of model matrix factorization describing the influence of nonlinear terms, which allowed to introduce structural constraints in the form of linear matrix inequalities, is proposed. To suppress the disturbances influence simulating unknown but bounded external demand, while ensuring robust stability of the closed-loop system, is used the invariant ellipsoids technique, which allowed to formulate the control problem in terms of linear matrix inequalities. As a result the control synthesis problem is reduced to a sequence of one-dimensional convex optimization problems and semi-definite programming. As an example, a fragment of the Kharkiv drinking water distribution system is consider.

On the structure of generalized plant convexifying static [formula omitted] control problems

This paper shows that, under specific structures of generalized plants, the set of static controllers satisfying internal stability and a certain level of H∞ performance becomes convex. More precisely, we characterize such static H∞ controllers by an LMI with controller variables being kept directly as decision variables. The structural conditions on the generalized plant are not too strict, and we show that generalized plants corresponding to a sort of mixed sensitivity problems indeed satisfy these conditions. For the generalized plants of interest, we further prove that full-order dynamical H∞ controllers can be characterized by an LMI with a simple change of variables. In stark contrast to the known LMI-based H∞ controller synthesis, the change of variables is free from the coefficient matrices of the generalized plant and this property is promising when dealing with a variety of robust control problems. Related issues such as robust controller synthesis against real parametric uncertainties are also discussed.

Delay‐dependent dissipative control for a class of non‐linear system via Takagi–Sugeno fuzzy descriptor model with time delay

This paper studies the dissipative control problems for the non-linear descriptor system via a Takagi-Sugeno descriptor model with time delay and uncertainties. The considered systems are not necessarily regular or impulse free. Using the free-weighting-matrix approach combined with the developed linear matrix inequality techniques, the authors proposed an improved delay-dependent stability criterion to guarantee the system to be admissible. Based on this criterion, the solvable conditions for the existence of dissipative controller are derived, which guarantees that the closed-loop system is not only admissible but also strictly dissipative for all admissible uncertainties. The proposed method is more suitable for the robust stability analysis and control synthesis. Moreover, different control processes can be achieved for the targeted systems in the same design process. Therefore it could potentially reduce cost and time in the controller design for an actual physical system. The authors perform simulations to validate the obtained method for practical examples.

Robust Control Synthesis of Polynomial Nonlinear Systems Using Sum of Squares Technique

Robust Control Synthesis of Polynomial Nonlinear Systems Using Sum of Squares Technique

Integrated Robust Optimal Design Using Bilinear Matrix Inequality Approach Via Sensitivity Minimization

A novel integrated robust control synthesis methodology is presented here which combines a traditional sensitivity theory with relatively new advancements in bilinear matrix inequality (BMI) constrained optimization problems. The proposed methodology is demonstrated using a numerical example of integrated control design problem for combine harvester header linkage. The integrated design methodology presented is compared with a traditional sequential design method and the results show that the proposed methodology provides a viable alternative for robust controller synthesis and often times offers even a better performance than competing methods.

A sum of squares approach to robust PI controller synthesis for a class of polynomial multi-input multi-output nonlinear systems

This paper presents a new algorithmic method to design PI controller for a general class of nonlinear polynomial systems. Design procedure can take place on certain or uncertain nonlinear model of plant and is based on sum of squares optimization.The so-called density function is employed to formulate the design problem as a convex optimization program in the sum of squares form. Robustness of design is guaranteed by taking parametric uncertainty into account with an approach similar to that of generalized \({\mathcal {S}}\)-Procedure. Validity and applicability of the proposed methods are verified via numerical simulations. The method presented here for PI controller design is not based on local linearization and works globally. Derived stability conditions overcome several drawbacks seen in previous results, such as depending on a linearized model or a stable model. Furthermore, employing sum of squares technique makes it possible to derive stability conditions with least conservatism and directly design controller for polynomial affine nonlinear systems.

Robust Satellite Formation Flying Through Online Trajectory Optimization using LQR and Neural Networks

Abstract Utilizing the well-established linear quadratic regulator (LQR) theory and augmenting it with online trained neural networks, an innovative nonlinear online trajectory optimization technique is presented in this paper. Neural networks are trained online using close form expression for weight update rule and do not require any iterative process. The overall structure leads to robust optimal control synthesis and works well despite the presence of un-modeled dynamics. This technique is subsequently applied to the challenging problem of satellite formation ying. Simulation studies show that the presented control synthesis approach is able to ensure close formation ying catering for large initial separation, high eccentricity orbits, uncertain semi-major axis of chief satellite and J 2 gravitational e_ects, which is usually considered as an exogenous perturbation.

Robust resilient controllers synthesis for uncertain fractional-order large-scale interconnected system

The problem of the decentralized stabilization for fractional order large-scale interconnected uncertain system with norm-bounded parametric uncertainties and controller gain perturbations is studied. It is solved under two circumstances: one is under the additive controller gain perturbations; the other is under the multiplicative ones. Sufficient conditions on the decentralized stabilization of fractional order large-scale interconnected system with a commensurate order 0<α<1 are established by applying a complex Lyapunov inequality method. The state feedback non-fragile controller designs for fractional order large-scale interconnected uncertain system under the two classes of gain perturbations are obtained in terms of solutions to LMIs. Numerical examples are used to illustrate the effectiveness of the proposed method.

Possibilities of using robust regulators for technological facilities

The class of non-stationary , multidimensional and multiply connected facilities , in particular, three-column distillation-rectification unit (DRU) of indirect action , which is characterized by complex hydrodynamic, mass- and heat exchange processes, is considered in the paper. For effective control of the class of facilities, a robust approach was selected , since the purpose of robust control synthesis is ensuring the required system quality , regardless of possible errors and changes in system parameters. The main objective of robust control is guaranteed control in conditions of incomplete priori information about the object, ensuring the system stability and maintaining its quality in the presence of all types of uncertainties which are studied and clearly identified for the DRU. The aim of the study is the use of robust approach for optimal control of the selected class of facilities to guarantee quality and stability of automated control system in cases of emergency situations of technological regime.

Flight and Wind-Tunnel Tests of Closed-Loop Active Flow Control

Closed-loop active flow control is applied in wind-tunnel tests to an industry-relevant civil aircraft half-model designed by Airbus and in full-scale free-flight experiments with a Stemme S10 glider. The focus of this contribution is on closed-loop control. Moreover, it is shown that our approach can be used for very different setups. For this, the modeling of the dynamic responses of the two systems and the synthesis of robust controllers are compared. For the highly three-dimensional wind-tunnel model, differential pressures are used as surrogate control variables as a correlation with the lift can be described by a lookup table. Two control inputs, pulsed blowing, and two output variables are exploited. In the glider study, with a profile that experiences a mostly two-dimensional flow, an approximate pressure gradient is used instead as a single output to avoid the necessity of such a lookup table. Active flow control is done again, exploiting pulsed blowing. For the controller synthesis, both in the single-input single-output and in the multivariable cases, the same approach is used, showing its versatility. In both setups, the closed-loop controllers succeed in adjusting the control inputs such that changing reference signals are followed, and the influence of disturbances are attenuated. For the civil aircraft model, completely new landing scenarios can be proposed using the closed-loop controller.

Solving Large-Scale Robust Stability Problems by Exploiting the Parallel Structure of Polya's Theorem

In this paper, we propose a distributed computing approach to solving large-scale robust stability problems on the simplex. Our approach is to formulate the robust stability problem as an optimization problem with polynomial variables and polynomial inequality constraints. We use Polya's theorem to convert the polynomial optimization problem to a set of highly structured Linear Matrix Inequalities (LMIs). We then use a slight modification of a common interior-point primal-dual algorithm to solve the structured LMI constraints. This yields a set of extremely large yet structured computations. We then map the structure of the computations to a decentralized computing environment consisting of independent processing nodes with a structured adjacency matrix. The result is an algorithm which can solve the robust stability problem with the same per-core complexity as the deterministic stability problem with a conservatism which is only a function of the number of processors available. Numerical tests on cluster computers and supercomputers demonstrate the ability of the algorithm to efficiently utilize hundreds and potentially thousands of processors and analyze systems with 100+ dimensional state-space. The proposed algorithms can be extended to perform stability analysis of nonlinear systems and robust controller synthesis.

Iterative procedure for the synthesis of an optimal robust PID controller

The article describes the method of calculation of robust controller in automatic control system with the internal model, that allows to significantly simplify the calculation of the regulator settings.

IQC-synthesis with general dynamic multipliers

SUMMARY Analogously to the existing μ-synthesis tools, we propose an alternative algorithm for the systematic design of robust controllers based on an iteration of standard nominal controller synthesis and integral quadratic constraint (IQC) analysis with general dynamic multipliers. The suggested algorithm enables us to perform robust controller synthesis for a significantly larger class of uncertainties if compared with the existing methods. Indeed, while the classical approaches are restricted to the use of real/complex time invariant or arbitrarily fast time-varying parametric uncertainties, the IQC framework also offers, for example, the possibility to efficiently handle sector-bounded and slope restricted nonlinearities or time-varying parametric uncertainties and uncertain time-varying time-delays, both with bounds on the rate-of-variation. Secondly, in contrast to the classical approaches, the proposed techniques completely avoid gridding and curve-fitting. We present new insights that allow us to reformulate the robust IQC analysis LMIs into a standard quadratic performance problem. This enables us to generate suitable initial conditions for each subsequent iteration step. Depending on the size of the problem, this can significantly speed up the synthesis process. The results are illustrated by means of two numerical examples. Copyright © 2013 John Wiley & Sons, Ltd.

Robust Control Synthesis of Polynomial Nonlinear Systems Using Sum of Squares Technique

In this paper, sum of squares (SOS) technique is used to analyze the robust state feedback synthesis problem for a class of uncertain affine nonlinear systems with polynomial vector fields. Sufficient conditions are given to obtain the solutions to the above control problem either without or with guaranteed cost or H∞performance objectives. Moreover, such solvable conditions can be formulated as SOS programming problems in terms of state dependent linear matrix inequalities (LMIs) which can be dealt with by the SOS technique directly. Besides, an idea is provided to describe the inverse of polynomial or even rational matrices by introducing some extra polynomials. A numerical example is presented to illustrate the effectiveness of the approach.

Robust observer‐based control design for uncertain singular systems with time‐delay

SUMMARYThis paper is concerned with the stability analysis and robust dynamic output feedback controller synthesis for uncertain continuous singular systems with time‐delay. First, on the basis of the Lyapunov functional method and by resorting to the delay‐partition technique, improved delay‐dependent sufficient conditions are presented to ensure the nominal unforced system to be admissible (i.e., to be regular, impulse‐free, and stable). Second, with the help of the obtained admissibility criterion, an observer‐based controller is designed by solving a set of LMIs. Finally, the validity and applicability of the proposed approach is shown by examples. Copyright © 2013 John Wiley &amp; Sons, Ltd.