H

This paper is concerned with H∞ static output tracking control of nonlinear systems with one-sided Lipschitz condition. The dimensions of system model and reference model may be different. A static output feedback controller is designed to guarantee that the system output asymptotically tracks the reference output with H∞ disturbance rejection level. A new sufficient condition is derived to obtain the static output feedback gain by linear matrix inequality (LMI), and no equality constraints can be needed. Finally, an example is given to illustrate the effectiveness of the proposed method

Adaptive neural network tracking control for underactuated systems with matched and mismatched disturbances

This paper studies neural network-based tracking control of underactuated systems with unknown parameters and with matched and mismatched disturbances. Novel adaptive control schemes are proposed with the utilization of multi-layer neural networks, adaptive control and variable structure strategies to cope with the uncertainties containing approximation errors, unknown base parameters and time-varying matched and mismatched external disturbances. Novel auxiliary control variables are designed to establish the controllability of the non-collocated subset of the underactuated systems. The approximation errors and the matched and mismatched external disturbances are efficiently counteracted by appropriate design of robust compensators. Stability and convergence of the time-varying reference trajectory are shown in the sense of Lyapunov. The parameter updating laws for the designed control schemes are derived using the projection approach to reduce the tracking error as small as desired. Unknown dynamics of the non-collocated subset is approximated through neural networks within a local region. Finally, simulation studies on an underactuated manipulator and an underactuated vibro-driven system are conducted to verify the effectiveness of the proposed control schemes

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

Uniform finite time stabilisation of non-smooth and variable structure systems with resets

This thesis studies uniform finite time stabilisation of uncertain variable structure and non-smooth systems with resets. Control of unilaterally constrained systems is a challenging area that requires an understanding of the underlying mechanics that give rise to reset or jumps while synthesizing stabilizing controllers. Discontinuous systems with resets are studied in various disciplines. Resets in states are hard nonlinearities. This thesis bridges non-smooth Lyapunov analysis, the quasi-homogeneity of differential inclusions and uniform finite time stability for a class of impact mechanical systems. Robust control synthesis based on second order sliding mode is undertaken in the presence of both impacts with finite accumulation time and persisting disturbances. Unlike existing work described in the literature, the Lyapunov analysis does not depend on the jumps in the state while also establishing proofs of uniform finite time stability. Orbital stabilization of fully actuated mechanical systems is established in the case of persisting impacts with an a priori guarantee of finite time convergence between t he periodic impacts. The distinguishing features of second order sliding mode controllers are their simplicity and robustness. Increasing research interest in the area has been complemented by recent advances in Lyapullov based frameworks which highlight the finite time Convergence property. This thesis computes the upper bound on the finite settling time of a second order sliding mode controller. Different to the latest advances in the area, a key contribution of this thesis is the theoretical proof of the fact that finite settling time of a second order sliding mode controller tends to zero when gains tend to infinity. This insight of the limiting behaviour forms the basis for solving the converse problem of finding an explicit a priori tuning formula for the gain parameters of the controller when and arbitrary finite settling time is given. These results play a central role ill the analysis of impact mechanical systems. Another key contribution of the thesis is that it extends the above results on variable structure systems with and without resets to non-smooth systems arising from continuous finite time controllers while proving uniform finite time stability. Finally, two applications are presented. The first application applies the above theoretical developments to the problem of orbital stabilization of a fully actuated seven link biped robot which is a nonlinear system with periodic impacts. The tuning of the controller gains leads to finite time convergence of the tracking errors between impacts while being robust to disturbances. The second application reports the outcome of an experiment with a continuous finite time controller

Regelungstheorie

The workshop “Regelungstheorie” (control theory) covered a broad variety of topics that were either concerned with fundamental mathematical aspects of control or with its strong impact in various fields of engineering

Modelling and Adaptive Control; Proceedings of an IIASA Conference, Sopron, Hungary, July 1986

One of the main purposes of the workshop on Modelling and Adaptive Control at Sopron, Hungary, was to give an overview of both traditional and recent approaches to the twin theories of modelling and control which ultimately must incorporate some degree of uncertainty. The broad spectrum of processes for which solutions of some of these problems were proposed was itself a testament to the vitality of research on these fundamental issues. In particular, these proceedings contain new methods for the modelling and control of discrete event systems, linear systems, nonlinear dynamics and stochastic processes

Optimization Algorithms as Robust Feedback Controllers

Mathematical optimization is one of the cornerstones of modern engineering research and practice. Yet, throughout all application domains, mathematical optimization is, for the most part, considered to be a numerical discipline. Optimization problems are formulated to be solved numerically with specific algorithms running on microprocessors. An emerging alternative is to view optimization algorithms as dynamical systems. Besides being insightful in itself, this perspective liberates optimization methods from specific numerical and algorithmic aspects and opens up new possibilities to endow complex real-world systems with sophisticated self-optimizing behavior. Towards this goal, it is necessary to understand how numerical optimization algorithms can be converted into feedback controllers to enable robust "closed-loop optimization". In this article, we focus on recent control designs under the name of "feedback-based optimization" which implement optimization algorithms directly in closed loop with physical systems. In addition to a brief overview of selected continuous-time dynamical systems for optimization, our particular emphasis in this survey lies on closed-loop stability as well as the robust enforcement of physical and operational constraints in closed-loop implementations. To bypass accessing partial model information of physical systems, we further elaborate on fully data-driven and model-free operations. We highlight an emerging application in autonomous reserve dispatch in power systems, where the theory has transitioned to practice by now. We also provide short expository reviews of pioneering applications in communication networks and electricity grids, as well as related research streams, including extremum seeking and pertinent methods from model predictive and process control, to facilitate high-level comparisons with the main topic of this survey