Control of Systems with Limited Capacity

Virtually all real life systems are such that they present some kind of limitation on one or many of its variables, physical quantities. These systems are designated in this thesis as systems with limited capacity. This work is treating control related problems of a subclass of such systems, where the limitation is a critical factor. The thesis is composed of four parts. The first part is treating the control of tire slip in a braking car. The Anti-lock Braking System (ABS) is an important component of a complex steering system for the modern car. In the latest generation of brake-by-wire systems, the controllers have to maintain a specified tire slip for each wheel during braking. This thesis proposes a design model and based on that a hybrid controller that regulates the tire-slip. Simulation and results from drive tests are presented. In the second part, a design method for robust PID controllers is presented for a class of systems with limited capacity. Robustness is ensured with respect to a cone bounded static nonlinearity acting on the plant. Additional constraints on maximum sensitivity are also considered. The design procedure has been successfully applied in the synthesis of the proposed ABS controller. The third part studies the trajectory convergence for a general class of nonlinear systems. The servo problem for piecewise linear systems is presented. Convex optimization is used to describe the behavior of system trajectories of a piecewise linear system with respect to some input signals. The obtained results are then applied for the study of anti-windup compensators. The last part of the thesis is treating the problem of voltage stability in power systems. Voltage at the load end of a power system has to be controlled within prescribed tolerances. In case of emergencies such as sudden line failures, this task ca n be very challenging. The main contribution of this chapter is a method for improving the stability properties of the power system by dynamic compensation of the reference load voltage. Moreover, a complete compensation scheme is proposed where load shedding is the secondary control variable. This control scheme is shown to stabilize different power system models

Feature-based motion control for near-repetitive structures

In many manufacturing processes, production steps are carried out on repetitive structures which consist of identical features placed in a repetitive pattern. In the production of these repetitive structures one or more consecutive steps are carried out on the features to create the final product. Key to obtaining a high product quality is to position the tool with respect to each feature of the repetitive structure with a high accuracy. In current industrial practice, local position sensors such as motor encoders are used to separately measure the metric position of the tool and the stage where the repetitive structure is on. Here, the final accuracy of alignment directly relies on assumptions like thermal stability, infinite machine frame stiffness and constant pitch between successive features. As the size of these repetitive structures is growing, often these assumptions are difficult to satisfy in practice. The main goal of this thesis is to design control approaches for accurately positioning the tool with respect to the features, without the need of the aforementioned assumptions. In this thesis, visual servoing, i.e., using machine vision data in the servo loop to control the motion of a system, is used for controlling the relative position between the tool and the features. By using vision as a measurement device the relevant dynamics and disturbances are therefore measurable and can be accounted for in a non-collocated control setting. In many cases, the pitch between features is subject to small imperfections, e.g., due to the finite accuracy of preceding process steps or thermal expansion. Therefore, the distance between two features is unknown a priori, such that setpoints can not be constructed a priori. In this thesis, a novel feature-based position measurement is proposed, with the advantage that the feature-based target position of every feature is known a priori. Motion setpoints can be defined from feature to feature without knowing the exact absolute metric position of the features beforehand. Next to feature-to-feature movements, process steps involving movements with respect to the features, e.g., engraving or cutting, are implemented to increase the versatility of the movements. Final positioning accuracies of 10 µm are attained. For feature-to-feature movements with varying distances between the features a novel feedforward control strategy is developed based on iterative learning control (ILC) techniques. In this case, metric setpoints from feature to feature are constructed by scaling a nominal setpoint to handle the pitch imperfections. These scale varying setpoints will be applied during the learning process, while second order ILC is used to relax the classical ILC boundary of setpoints being the same every trial. The final position accuracy is within 5 µm, while scale varying setpoints are applied. The proposed control design approaches are validated in practice on an industrial application, where the task is to position a tool with respect to discrete semiconductors of a wafer. A visual servoing setup capable of attaining a 1 kHz frame rate is realized. It consists of an xy-stage on which a wafer is clamped which contains the discrete semiconductor products. A camera looks down onto the wafer and is used for position feedback. The time delay of the system is 2.5 ms and the variation of the position measurement is 0.3 µm (3s)

High performance DSP-based servo drive control for a limited-angle torque motor

This thesis describes the analysis, design and implementation of a high performance DSP-based servo drive for a limited-angle torque motor used in thermal imaging applications. A limited-angle torque motor is an electromagnetic actuator based on the Laws' relay principle, and in the present application the rotation required was from - 10° to + 10° in 16 ms, with a flyback period of 4 ms. To ensure good quality picture reproduction, an exceptionally high linearity of ±0.02 ° was necessary throughout the forward sweep. In addition, the drive voltage to the exciting winding of the motor should be less than the +35 V ceiling of the drive amplifier. A research survey shows that little literature was available, probably due to the commercial sensitivity of many of the applications for torque motors. A detailed mathematical model of the motor drive, including high-order linear dynamics and the significant nonlinear characteristics, was developed to provide an insight into the overall system behaviour. The proposed control scheme uses a multicompensator, multi-loop linear controller, to reshape substantially the motor response characteristic, with a non-linear adaptive gain-scheduled controller to compensate effectively for the nonlinear variations of the motor parameters. The scheme demonstrates that a demanding nonlinear control system may be conveniently analysed and synthesised using frequency-domain methods, and that the design techniques may be reliably applied to similar electro-mechanical systems required to track a repetitive waveform. A prototype drive system was designed, constructed and tested during the course of the research. The drive system comprises a DSP-based digital controller, a linear power amplifier and the feedback signal conditioning circuit necessary for the closed-loop control. A switch-mode amplifier was also built, evaluated and compared with the linear amplifier. It was shown that the overall performance of the linear amplifier was superior to that of the switch-mode amplifier for the present application. The control software was developed using the structured programming method, with the continuous controller converted to digital form using the bilinear transform. The 6- operator was used rather than the z-operator, since it is more advantageous for high speed sampling systems. The gain-scheduled control was implemented by developing a schedule table, which is controlled by the DSP program to update continuously the controller parameters in synchronism with the periodic scanning of the motor. The experimental results show excellent agreement with the simulated results, with linearity of ±0.05 ° achieved throughout the forward sweep. Although this did not quite meet the very demanding specifications due to the limitations of the experimental drive system, it clearly demonstrates the effectiveness of the proposed control scheme. The discrepancies between simulated and experimental results are analyzed and discussed, the control design method is reviewed, and detailed suggestions are presented for further work which may improve the drive performance

System analysis, modelling and control with polytopic linear models

This research investigates the suitability of Polytopic Linear Models (PLMs) for the analysis, modelling and control of a class of nonlinear dynamical systems. The PLM structure is introduced as an approximate and alternative description of nonlinear dynamical systems for the benefit of system analysis and controller design. The model structure possesses three properties that we would like to exploit. Firstly, a PLM is build upon a number of linear models, each one of which describes the system locally within a so-called operating regime. If these models are combined in an appropriate way, that is by taking operating point dependent convex combinations of parameter values that belong to the different linear models, then a PLM will result. Consequently, the parameter values of a PLM vary within a polytope, and the vertices of this polytope are the parameter values that belong to the different linear models. A PLM owes its name to this feature. Accordingly, a PLM can be interpreted on the basis of a regime decomposition. Secondly, since a PLM is based on several linear models, it is possible to describe the nonlinear system more globally compared to only a single linear model. Thirdly, it is demonstrated that, under the appropriate conditions, nonlinear systems can be approximated arbitrary close by a PLM, parametrized with a finite number of parameters. There will be given an upper bound for the number of required parameters, that is sufficient to achieve the prescribed desired accuracy of the approximation. An important motivation for considering PLMs rests on its structural similarities with linear models. Linear systems are well understood, and the accompanying system and control theory is well developed. Whether or not the control related system properties such as stability, controllability etcetera, are fulfilled, can be demonstrated by means of (often relatively simple) mathematical manipulations on the linear system’s parameterization. Controller design can often be automated and founded on the parameterization and the control objective. Think of control laws based on stability, optimality and so on. For nonlinear systems this is only partly the case, and therefore further development of system and control theory is of major importance. In view of the similarities between a linear model and a PLM, the expectation exists that one can benefit from (results and concepts of) the well developed linear system and control theory. This hypothesis is partly confirmed by the results of this study. Under the appropriate conditions, and through a simple analysis of the parametrization of a PLM, it is possible to establish from a control perspective relevant system properties. One of these properties is stability. Under the appropriate conditions stability of the PLM implies stability of the system. Moreover, a few easy to check conditions are derived concerning the notion of controllability and observability. It has to be noticed however, that these conditions apply to a class of PLMs of which the structure is further restricted. The determination of system properties from a PLM is done with the intention to derive a suitable model, and in particular to design a model based controller. This study describes several constructive methods that aim at building a PLM representation of the real system. On the basis of a PLM several control laws are formulated. The main objective of these control laws is to stabilize the system in a desired operating point. A few computerized stabilizing control designs, that additionally aim at optimality or robustness, are the outcome of this research. The entire route of representing a system with an approximate PLM, subsequently analyzing the PLM, and finally controlling the system by a PLM based control design is illustrated by means of several examples. These examples include experimental as well as simulation studies, and nonlinear dynamic (mechanical) systems are the subject of research

Correct-By-Construction Control Synthesis for Systems with Disturbance and Uncertainty

This dissertation focuses on correct-by-construction control synthesis for Cyber-Physical Systems (CPS) under model uncertainty and disturbance. CPSs are systems that interact with the physical world and perform complicated dynamic tasks where safety is often the overriding factor. Correct-by-construction control synthesis is a concept that provides formal performance guarantees to closed-loop systems by rigorous mathematic reasoning. Since CPSs interact with the environment, disturbance and modeling uncertainty are critical to the success of the control synthesis. Disturbance and uncertainty may come from a variety of sources, such as exogenous disturbance, the disturbance caused by co-existing controllers and modeling uncertainty. To better accommodate the different types of disturbance and uncertainty, the verification and control synthesis methods must be chosen accordingly. Four approaches are included in this dissertation. First, to deal with exogenous disturbance, a polar algorithm is developed to compute an avoidable set for obstacle avoidance. Second, a supervised learning based method is proposed to design a good student controller that has safety built-in and rarely triggers the intervention of the supervisory controller, thus targeting the design of the student controller. Third, to deal with the disturbance caused by co-existing controllers, a Lyapunov verification method is proposed to formally verify the safety of coexisting controllers while respecting the confidentiality requirement. Finally, a data-driven approach is proposed to deal with model uncertainty. A minimal robust control invariant set is computed for an uncertain dynamic system without a given model by first identifying the set of admissible models and then simultaneously computing the invariant set while selecting the optimal model. The proposed methods are applicable to many real-world applications and reflect the notion of using the structure of the system to achieve performance guarantees without being overly conservative.PHDMechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/145933/1/chenyx_1.pd

Computer Control: An Overview

Computer control is entering all facets of life from home electronics to production of different products and material. Many of the computers are embedded and thus ``hidden'' for the user. In many situations it is not necessary to know anything about computer control or real-time systems to implement a simple controller. There are, however, many situations where the result will be much better when the sampled-data aspects of the system are taken into consideration when the controller is designed. Also, it is very important that the real-time aspects are regarded. The real-time system influences the timing in the computer and can thus minimize latency and delays in the feedback controller. The paper introduces different aspects of computer-controlled systems from simple approximation of continuous time controllers to design aspects of optimal sampled-data controllers. We also point out some of the pitfalls of computer control and discusses the practical aspects as well as the implementation issues of computer control. Published as a Professional Briefs by IFAC

Modeling and analysis of a semi-active magneto-rheological damper suspension seat and controller synthesis

Whole body vibration in operational vehicles can cause serious musculo-skeletal disorders among the exposed workers. Consequently, considerable efforts have been made to protect vehicle operators from potentially harmful vibration. This thesis was aimed at the development of a semi-active suspension seat equipped with a magneto-rheological (MR) fluid damper. A damper controller was synthesized to minimize the vibration transmitted to the seated body and the frequency of end-stop impacts, which is known to induce high intensity vibration or shock motions to the seated occupant. A suspension seat was modeled by considering the kinematic non-linearity due to the cross-linkages and the damper link, while the cushion characteristics were linearized about the operating preload. The force-velocity properties of the MR damper were modeled by piecewise polynomial functions of applied current on the basis of the laboratory-measured data. The kineto-dynamic model of the suspension seat was thoroughly validated using the laboratory-measured responses under harmonic excitations in the 0.5 to 10Hz range. The performance characteristics of the passive suspension seat model were evaluated under different vehicular excitations in terms of frequency-weighted rms acceleration, vibration dose value (VDV), seat effective amplitude transmissibility (SEAT) and VDV ratio. These performance characteristics are also evaluated under amplified vehicular excitations in order to investigate the frequency as well as the potential suppression of end-stop impacts. The controller synthesis was realized in two stages: (1) attenuation of continuous vibration; and (2) suppression of end-stop impacts. Two different algorithms were explored in the first stage synthesis, which included a sky-hook control algorithm and a relative states feedback control algorithm. Each algorithm was further utilized in two different control current modulations. The performance potentials of each control synthesis were investigated using the 2 MATLAB Simulink platform under harmonic, transient, and random vehicular excitations in terms of SEAT and VDV ratio. One controller design (overall best suited for implementations) was subsequently implemented in a hardware-in-the-loop (HIL) test platform coupled with a MR-fluid damper mounted on an electro-hydraulic actuator that was linked to the HIL simulation platform. The semi-active suspension seat performance characteristics were further evaluated under different excitations using the selected control scheme. The results showed that the selected control scheme yielded SEAT and VDV ratio reductions in the 5 to 30% range depending upon the nature of excitations. The implementation of the second-stage controller, which was tested only by simulations, entirely eliminated the occurrence of end-stop impacts at nominal vibration level and attenuated the end-stop impact severity of three times amplified excitations by up to 10% . The results further suggested that the use of MR-fluid damper in suspension seat was most beneficial to city buses and class I earth moving vehicles amongst the selected inputs

Optimal workloop energetics of muscle-actuated systems

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2007.Includes bibliographical references (p. 117-122).Skeletal muscles are the primary actuators that power, stabilize and control locomotive and functional motor tasks in biological systems. It is well known that coordinated action and co-activation of multiple muscles give rise to desirable effects such as enhanced postural and dynamic stability. In this thesis, we study the role of muscle co-activation from an energetics perspective: Are there situations in which antagonist co-activation leads to enhanced power generation, and if so, what is the underlying mechanism? The mechanical energetics of muscles are traditionally characterized in terms of workloop measures where muscles are activated against oscillating, zero-admittance motion sources. We extend these measures to more natural, "mid-range" admittance loads, actuated by multiple muscles. Specifically, we set up the problem of a second-order mechanical system driven by a pair of antagonist muscles. This is the simplest problem where the influences of load dynamics and muscle co-activation on the output energetics may be investigated. To enable experimentation, a muscle testing apparatus capable of real-time servo emulation of the load is developed and utilized for identification and workloop measurements.(cont.) Using this apparatus, an experimentally identified model predicting muscle contractile force is proposed. Experimental data shows that with a simple Weiner structure, the model accounts for 74% (sigma = 5.6%) of the variance in muscle force, that force dependence on contraction velocity is minimal, and that a bilinear approximation of the output nonlinearity is warranted. Based on this model we investigate what electrical stimulation input gives rise to maximal power transfer for a particular load. This question is cast in an optimal control framework. Necessary conditions for optimality are derived and methods for computing solutions are presented. Solutions demonstrate that the optimal stimulation frequencies must include the effects of muscle impedances, and that optimal co-activation levels are indeed modulated to enable a pair of muscles to produce more work synergistically rather than individually. Pilot experimental data supporting these notions is presented. Finally, we interpret these results in the context of the familiar engineering notion of impedance matching. These results shed new light on the role of antagonist co-activation from an energetics perspective.by Walled A. Farahat.Ph.D

MATLAB

This excellent book represents the final part of three-volumes regarding MATLAB-based applications in almost every branch of science. The book consists of 19 excellent, insightful articles and the readers will find the results very useful to their work. In particular, the book consists of three parts, the first one is devoted to mathematical methods in the applied sciences by using MATLAB, the second is devoted to MATLAB applications of general interest and the third one discusses MATLAB for educational purposes. This collection of high quality articles, refers to a large range of professional fields and can be used for science as well as for various educational purposes

Nondeterministic hybrid dynamical systems

This thesis is concerned with the analysis, control and identification of hybrid dynamical systems. The main focus is on a particular class of hybrid systems consisting of linear subsystems. The discrete dynamic, i.e., the change between subsystems, is unknown or nondeterministic and cannot be influenced, i.e. controlled, directly. However changes in the discrete dynamic can be detected immediately, such that the current dynamic (subsystem) is known. In order to motivate the study of hybrid systems and show the merits of hybrid control theory, an example is given. It is shown that real world systems like Anti Locking Brakes (ABS) are naturally modelled by such a class of linear hybrids systems. It is shown that purely continuous feedback is not suitable since it cannot achieve maximum braking performance. A hybrid control strategy, which overcomes this problem, is presented. For this class of linear hybrid system with unknown discrete dynamic, a framework for robust control is established. The analysis methodology developed gives a robustness radius such that the stability under parameter variations can be analysed. The controller synthesis procedure is illustrated in a practical example where the control for an active suspension of a car is designed. Optimal control for this class of hybrid system is introduced. It is shows how a control law is obtained which minimises a quadratic performance index. The synthesis procedure is stated in terms of a convex optimisation problem using linear matrix inequalities (LMI). The solution of the LMI not only returns the controller but also the performance bound. Since the proposed controller structures require knowledge of the continuous state, an observer design is proposed. It is shown that the estimation error converges quadratically while minimising the covariance of the estimation error. This is similar to the Kalman filter for discrete or continuous time systems. Further, we show that the synthesis of the observer can be cast into an LMI, which conveniently solves the synthesis problem