H∞ controller design for networked predictive control systems based on the average dwell-time approach

This brief focuses on the problem of H∞ control for a class of networked control systems with time-varying delay in both forward and backward channels. Based on the average dwell-time method, a novel delay-compensation strategy is proposed by appropriately assigning the subsystem or designing the switching signals. Combined with this strategy, an improved predictive controller design approach in which the controller gain varies with the delay is presented to guarantee that the closed-loop system is exponentially stable with an H∞-norm bound for a class of switching signal in terms of nonlinear matrix inequalities. Furthermore, an iterative algorithm is presented to solve these nonlinear matrix inequalities to obtain a suboptimal minimum disturbance attenuation level. A numerical example illustrates the effectiveness of the proposed method

Robust magnetic bearing control using stabilizing dynamical compensators

Abstract—This paper considers the robust control of an active radial magnetic bearing system, having a homopolar, external rotor topology, which is used to support an annular fiber composite flywheel rim. A first-order dynamical compensator, which uses only position feedback information, is used for control, its design being based on a linearized one-dimensional second-order model which is treated as an interval system in order to cope with parameter uncertainties. Through robust stability analysis, a parameterization of all first-order robustly stabilizing dynamical compensators for the interval system is initially obtained. Then, by appropriate selection of the free parameters in the robust controller, the H2 norm of the disturbance-output transfer function is made arbitrarily small over the system parameter intervals, and the norm of the input–output transfer function is made arbitrarily close to a lower bound. Simulation and experimental results demonstrate both stability and performance robustness of the developed controller

μ-Dependent model reduction for uncertain discrete-time switched linear systems with average dwell time

In this article, the model reduction problem for a class of discrete-time polytopic uncertain switched linear systems with average dwell time switching is investigated. The stability criterion for general discrete-time switched systems is first explored, and a μ-dependent approach is then introduced for the considered systems to the model reduction solution. A reduced-order model is constructed and its corresponding existence conditions are derived via LMI formulation. The admissible switching signals and the desired reduced model matrices are accordingly obtained from such conditions such that the resulting model error system is robustly exponentially stable and has an exponential H∞ performance. A numerical example is presented to demonstrate the potential and effectiveness of the developed theoretical results

Filtering for nonlinear genetic regulatory networks with stochastic disturbances

In this paper, the filtering problem is investigated for nonlinear genetic regulatory networks with stochastic disturbances and time delays, where the nonlinear function describing the feedback regulation is assumed to satisfy the sector condition, the stochastic perturbation is in the form of a scalar Brownian motion, and the time delays exist in both the translation process and the feedback regulation process. The purpose of the addressed filtering problem is to estimate the true concentrations of the mRNA and protein. Specifically, we are interested in designing a linear filter such that, in the presence of time delays, stochastic disturbances as well as sector nonlinearities, the filtering dynamics of state estimation for the stochastic genetic regulatory network is exponentially mean square stable with a prescribed decay rate lower bound beta. By using the linear matrix inequality (LMI) technique, sufficient conditions are first derived for ensuring the desired filtering performance for the gene regulatory model, and the filter gain is then characterized in terms of the solution to an LMI, which can be easily solved by using standard software packages. A simulation example is exploited in order to illustrate the effectiveness of the proposed design procedures

Output-feedback design for non-smooth mechanical systems : control synthesis and experiments

In this thesis, the focus is on two control problems for non-smooth systems. Firstly, the disturbance attenuation problem for piecewise linear (PWL) and piecewise affine (PWA) systems is studied. Here, we focus on applications in the field of perturbed flexible mechanical systems with PWL restoring characteristics. Secondly, the stabilization problem for Lur’e type systems with set-valued nonlinearities is examined. In the latter context, the focus is on the application area of mechanical systems with set-valued friction characteristics, where the friction is non-collocated with the control action. In this thesis, in order to deal with both the disturbance attenuation problem and the stabilization problem, observer-based output-feedback control strategies are proposed. More specifically, the disturbance attenuation problem for perturbed PWL and PWA mechanical systems is an important control problem. Namely, the attenuation of the disturbances acting on these systems is important because it avoids damages to the structures and allows for increased system performance. Classical examples of mechanical systems with PWL and PWA restoring characteristics are tower cranes, suspension bridges, snubbers on solar panels on satellites, floating platforms for oil exploration, etc. Therefore, a controller design strategy is proposed for a class of perturbed PWL/PWA systems based on the notions of convergence and input-to-state convergence. The control design aims at the performance of such control designs in terms of disturbance attenuation for the specific class of periodic disturbances and the more general class of bounded disturbances. Roughly speaking, a system that is convergent, has, for each bounded disturbance, a unique globally asymptotically stable steady-state solution that is bounded for all time. A system is input-to-state convergent for a class of bounded disturbances if it is convergent and ISS with respect to the system’s unique steady-state solution. The input-to-state convergence property is instrumental in constructing output-feedback schemes. In the present work, we render a system convergent by means of feedback. To guarantee the practical applicability of the convergence-based controllers, a saturation constraint is proposed that provides a guaranteed upper bound on the control input, given an upper bound for the disturbances and a set of initial conditions. Next, an ultimate bound for the system state given a bound on the disturbances is proposed. Finally, performance measures based on computed steady-state responses for a specific class of disturbances (in our case harmonic disturbances) are presented. The motivation for the choice of harmonic disturbances lies in the fact that in engineering practice many disturbances can be approximated by a finite sum of harmonic signals (or are even harmonic as in systems with mass-unbalance). The ultimate objective of this part of the thesis is the implementation of the controller design strategy in an experimental environment, which implies that only measurements of a limited number of state variables will be available. Therefore, observers for PWL/PWA systems are used and a result that combines the controller and the observer in an outputfeedback strategy is provided. The convergent-based controller design strategy is applied to an experimental piecewise linear system and its effectiveness is shown in experiments. The stabilization of mechanical systems with friction is another challenging unsolved control problem because the presence of friction can induce unwanted phenomena such as self-sustained vibrations, chatter and squeal. These phenomena are unwanted in many engineering applications because they can destabilize a system and/or limit the system performance. Classical examples of mechanical systems with friction are industrial robots, drilling rigs, turbine blade dampers, accurate mirror positioning systems on satellites, printers and many more. Therefore, a control design strategy is proposed for a class of discontinuous systems; namely Lur’e systems with set-valued mappings. Here the focus is on the application area of mechanical systems with discontinuous friction. These systems exhibit unwanted (stick-slip) limit cycling which we aim to avoid entirely by the control design. In this work, we consider the problem of noncollocated friction and actuation, which rules out the application of common friction compensation techniques. The control design strategy proposed here is based on the notion of passivity and the Popov criterion. In addition to that, it is shown that the resulting closed-loop system is robust with respect to uncertainties in the discontinuous friction model under some mild constraints for the model that describes the friction. Once again, the aim is to implement this strategy on a mechanical experimental set-up with limited measurements. Therefore, an observer for Lur’e systems with multi-valued mappings is used as a state estimator and a result that combines the controller and the observer in an output-feedback strategy is provided. The passivity-based controller design strategy is implemented on a dynamic rotor system with friction in one of its components. The implemented output-feedback controller is evaluated in both simulations and experiments. Generally speaking, to show the strengths, weaknesses and potential of output-feedback controllers beyond their theoretical importance, it is indispensable to evaluate them in experimental and industrial setups. As such the presented case studies can be considered as benchmarks for the proposed observer-based controller designs for non-smooth and discontinuous systems. The value of non-smooth and discontinuous models and observer-based controllers is also evidenced by this work, as it demonstrates the effectiveness for real-life applications

Rapidly converging multichannel controllers for broadband noise and vibrations

Applications are given of a preconditioned adaptive algorithm for broadband multichannel active noise control. Based on state-space descriptions of the relevant transfer functions, the algorithm uses the inverse of the minimum-phase part of the secondary path in order to improve the speed of convergence. A further improvement of the convergence rate is obtained by using double control filters for elimination of adaptation loop delay. Regularization was found to be essential for robust operation. The particular regularization technique preserves the structure to eliminate the adaptation loop delay. Depending on the application at hand, a number of extensions are used for this algorithm, such as for applications with rapidly changing disturbance spectra, applications with large parametric uncertainty, applications with control of time-varying acoustic energy density

Robust H1 control for a class of switched nonlinear systems

This article is concerned with the robust H1 control problem of a class of switched nonlinear systems with norm-bounded time-varying uncertainties. The system considered in this class is composed of two parts: a uncertain linear switched part and a nonlinear part, which is also switched systems. Under the circumstances, that the H1 control problem of all subsystems are not all solvable, the switched feedback control law and the switching law are designed using the average dwell-time method. The corresponding closed-loop switched system is exponentially stable and achieves a weighted L2-gain

Topics in Automotive Rollover Prevention: Robust and Adaptive Switching Strategies for Estimation and Control

The main focus in this thesis is the analysis of alternative approaches for estimation and control of automotive vehicles based on sound theoretical principles. Of particular importance is the problem rollover prevention, which is an important problem plaguing vehicles with a high center of gravity (CG). Vehicle rollover is, statistically, the most dangerous accident type, and it is difficult to prevent it due to the time varying nature of the problem. Therefore, a major objective of the thesis is to develop the necessary theoretical and practical tools for the estimation and control of rollover based on robust and adaptive techniques that are stable with respect to parameter variations. Given this background, we first consider an implementation of the multiple model switching and tuning (MMST) algorithm for estimating the unknown parameters of automotive vehicles relevant to the roll and the lateral dynamics including the position of CG. This results in high performance estimation of the CG as well as other time varying parameters, which can be used in tuning of the active safety controllers in real time. We then look into automotive rollover prevention control based on a robust stable control design methodology. As part of this we introduce a dynamic version of the load transfer ratio (LTR) as a rollover detection criterion and then design robust controllers that take into account uncertainty in the CG position. As the next step we refine the controllers by integrating them with the multiple model switched CG position estimation algorithm. This results in adaptive controllers with higher performance than the robust counterparts. In the second half of the thesis we analyze extensions of certain theoretical results with important implications for switched systems. First we obtain a non-Lyapunov stability result for a certain class of linear discrete time switched systems. Based on this result, we suggest switched controller synthesis procedures for two roll dynamics enhancement control applications. One control design approach is related to modifying the dynamical response characteristics of the automotive vehicle while guaranteeing the switching stability under parametric variations. The other control synthesis method aims to obtain transient free reference tracking of vehicle roll dynamics subject to parametric switching. In a later discussion, we consider a particular decentralized control design procedure based on vector Lyapunov functions for simultaneous, and structurally robust model reference tracking of both the lateral and the roll dynamics of automotive vehicles. We show that this controller design approach guarantees the closed loop stability subject to certain types of structural uncertainty. Finally, assuming a purely theoretical pitch, and motivated by the problems considered during the course of the thesis, we give new stability results on common Lyapunov solution (CLS) existence for two classes of switching linear systems; one is concerned with switching pair of systems in companion form and with interval uncertainty, and the other is concerned with switching pair of companion matrices with general inertia. For both problems we give easily verifiable spectral conditions that are sufficient for the CLS existence. For proving the second result we also obtain a certain generalization of the classical Kalman-Yacubovic-Popov lemma for matrices with general inertia

Adaptive multichannel control of time-varying broadband noise and vibrations

This paper presents results obtained from a number of applications in which a recent adaptive algorithm for broadband multichannel active noise control is used. The core of the algorithm uses the inverse of the minimum-phase part of the secondary path for improvement of the speed of convergence. A further improvement of the speed of convergence is obtained by using double control filters for elimination of adaptation loop delay. Regularization was found to be necessary for robust operation. The regularization technique which is used preserves the structure to eliminate the adaptation loop delay. Depending on the application at hand, a number of extensions are used for this algorithm. For an application with rapidly changing disturbance spectra, the core algorithm was extended with an iterative affine projection scheme, leading to improved convergence rates as compared to the standard nomalized lms update rules. In another application, in which the influence of the parametric uncertainties was critical, the core algorithm was extended with low authority control loops operating at high sample rates. In addition, results of other applications are given, such as control of acoustic energy density and control of time-varying periodic and non-periodic vibrations

Robust Adaptive Control of Switched Systems

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