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

Ultimate boundedness of droop controlled Microgrids with secondary loops

In this paper we study theoretical properties of inverter-based microgrids controlled via primary and secondary loops. Stability of these microgrids has been the subject of a number of recent studies. Conventional approaches based on standard hierarchical control rely on time-scale separation between primary and secondary control loops to show local stability of equilibria. In this paper we show that (i) frequency regulation can be ensured without assuming time-scale separation and, (ii) ultimate boundedness of the trajectories starting inside a region of the state space can be guaranteed under a condition on the inverters power injection errors. The trajectory ultimate bound can be computed by simple iterations of a nonlinear mapping and provides a certificate of the overall performance of the controlled microgrid.Comment: 8 pages, 1 figur

Robust H2/H∞-state estimation for systems with error variance constraints: the continuous-time case

Copyright [1999] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.The paper is concerned with the state estimator design problem for perturbed linear continuous-time systems with H∞ norm and variance constraints. The perturbation is assumed to be time-invariant and norm-bounded and enters into both the state and measurement matrices. The problem we address is to design a linear state estimator such that, for all admissible measurable perturbations, the variance of the estimation error of each state is not more than the individual prespecified value, and the transfer function from disturbances to error state outputs satisfies the prespecified H∞ norm upper bound constraint, simultaneously. Existence conditions of the desired estimators are derived in terms of Riccati-type matrix inequalities, and the analytical expression of these estimators is also presented. A numerical example is provided to show the directness and effectiveness of the proposed design approac

A Framework for Phasor Measurement Placement in Hybrid State Estimation via Gauss-Newton

In this paper, we study the placement of Phasor Measurement Units (PMU) for enhancing hybrid state estimation via the traditional Gauss-Newton method, which uses measurements from both PMU devices and Supervisory Control and Data Acquisition (SCADA) systems. To compare the impact of PMU placements, we introduce a useful metric which accounts for three important requirements in power system state estimation: {\it convergence}, {\it observability} and {\it performance} (COP). Our COP metric can be used to evaluate the estimation performance and numerical stability of the state estimator, which is later used to optimize the PMU locations. In particular, we cast the optimal placement problem in a unified formulation as a semi-definite program (SDP) with integer variables and constraints that guarantee observability in case of measurements loss. Last but not least, we propose a relaxation scheme of the original integer-constrained SDP with randomization techniques, which closely approximates the optimum deployment. Simulations of the IEEE-30 and 118 systems corroborate our analysis, showing that the proposed scheme improves the convergence of the state estimator, while maintaining optimal asymptotic performance.Comment: accepted to IEEE Trans. on Power System

Convex Optimization In Identification Of Stable Non-Linear State Space Models

A new framework for nonlinear system identification is presented in terms of optimal fitting of stable nonlinear state space equations to input/output/state data, with a performance objective defined as a measure of robustness of the simulation error with respect to equation errors. Basic definitions and analytical results are presented. The utility of the method is illustrated on a simple simulation example as well as experimental recordings from a live neuron.Comment: 9 pages, 2 figure, elaboration of same-title paper in 49th IEEE Conference on Decision and Contro