Hybrid operator models for digitally implemented control systems

A method of analysis for digitally implemented (hybrid) control systems based on conic sector concepts from functional analysis was established. Data sampling is addressed

Multi-Input Multi-Output Repetitive Control Theory And Taylor Series Based Repetitive Control Design

Repetitive control (RC) systems aim to achieve zero tracking error when tracking a periodic command, or when tracking a constant command in the presence of a periodic disturbance, or both a periodic command and periodic disturbance. This dissertation presents a new approach using Taylor Series Expansion of the inverse system z-transfer function model to design Finite Impulse Response (FIR) repetitive controllers for single-input single-output (SISO) systems, and compares the designs obtained to those generated by optimization in the frequency domain. This approach is very simple, straightforward, and easy to use. It also supplies considerable insight, and gives understanding of the cause of the patterns for zero locations in the optimization based design. The approach forms a different and effective time domain design method, and it can also be used to guide the choice of parameters in performing in the frequency domain optimization design. Next, this dissertation presents the theoretical foundation for frequency based optimization design of repetitive control design for multi-input multi-output (MIMO) systems. A comprehensive stability theory for MIMO repetitive control is developed. A necessary and sufficient condition for asymptotic stability in MIMO RC is derived, and four sufficient conditions are created. One of these is the MIMO version of the approximate monotonic decay condition in SISO RC, and one is a necessary and sufficient condition for stability for all possible disturbance periods. An appropriate optimization criterion for direct MIMO is presented based on minimizing a Frobenius norm summed over frequencies from zero to Nyquist. This design process is very tractable, requiring only solution of a linear algebraic equation. An alternative approach reduces the problem to a set of SISO design problems, one for each input-output pair. The performances of the resulting designs are studied by extensive examples. Both approaches are seen to be able to create RC designs with fast monotonic decay of the tracking error. Finally, this dissertation presents an analysis of using an experiment design sequence for parameter identification based on the theory of iterative learning control (ILC), a sister field to repetitive control. This is suggested as an alternative to the results in optimal experiment design. Modified ILC laws that are intentionally non-robust to model errors are developed, as a way to fine tune the use of ILC for identification purposes. The non-robustness with respect to its ability to improve identification of system parameters when the model error is correct is studied. It is demonstrated that in many cases the approach makes the learning particularly sensitive to relatively small parameter errors in the model, but sensitivity is sometimes limited to parameter errors of a specific sign

Sinteza H-beskonačno regulatora s unaprijednom granom za kompenzaciju histereze kod piezoelektričnih aktuatora

Piezoelectric actuators, widely used in different micro/nanopositioning applications, generally exhibit nonlinear hysteresis characteristics. The compensation of hysteretic behavior of piezoelectric actuators is mandatory for precise micro/nanopositioning. In this paper, nonlinear hysteresis effect is first characterized using the Prandtl-Ishlinskii hysteresis model. The inverse of the Prandtl-Ishlinskii hysteresis model is employed as a feed-forward controller to compensate for hysteresis nonlinearities of the piezoelectric actuator. Slight hysteresis nonlinearity is still observed in the experimental results due to small mismatch between the identified hysteresis model and the measured hysteresis loop. To further enhance the performance of the piezoelectric actuator in terms of mitigation of hysteresis nonlinearity and precise reference tracking, advanced robust full-order as well as fixed-order H-infinity feedback controllers are designed and applied to this actuator in the presence of feed-forward compensator. The experimental results verify the effectiveness of the proposed control scheme in achieving the improved tracking performance with peak-to-peak tracking error of less than 1% for the desired displacement of 12 um with tracking frequency of 10 Hz.Piezoelektrični aktuatori, rasprostranjeni u različitim primjenama mikro/nanopozicioniranja, općenito su izloženi nelinearnim histereznim karakteristikama. Kompenzacija histereznog ponašanja piezoelektričnih aktuatora nužna je za precizno mikro/nanopozicioniranje. Inverzni Prandtl-Ishlinskii histerezni model korišten je za unaprijednu kompenzaciju histereznih nelinearnosti piezoelektričnog aktuatora. Neznatna histerezna nelinearnost još uvijek je vidljiva u eksperimentalnim rezultatima zbog malog neslaganja između identificiranog histereznog modela i mjerene histerezne petlje. Za daljnje poboljšanje performansi piezoelektričnog aktuatora u smislu smanjenja histerezne nelinearnosti i preciznog slijeđenja reference, napredni robusni H-beskonačno regulatori punog i određenog reda sintetizirani su i primijenjeni na ovaj aktuator uz prisutnost unaprijednog kompenzatora. Eksperimentalni rezultati potvrđuju efektivnost predložene upravljačke strukture u postizanju poboljšanih performansi slijeđenja, uz vršnu vrijednost pogreške manju od 1% za ciljani pomak od 12 um s frekvencijom slijeđenja od 10 Hz

State-Space Interpretation of Model Predictive Control

A model predictive control technique based on a step response model is developed using state estimation techniques. The standard step response model is extended so that integrating systems can be treated within the same framework. Based on the modified step response model, it is shown how the state estimation techniques from stochastic optimal control can be used to construct the optimal prediction vector without introducing significant additional numerical complexity. In the case of integrated or double integrated white noise disturbances filtered through general first-order dynamics and white measurement noise, the optimal filter gain is parametrized explicitly in terms of a single parameter between 0 and 1, thus removing the requirement for solving a Riccati equation and equipping the control system with useful on-line tuning parameters. Parallels are drawn to the existing MPC techniques such as Dynamic Matrix Control (DMC), Internal Model Control (IMC) and Generalized Predictive Control (GPC)

Frequency-Weighted Model Reduction with Applications to Structured Models

In this paper, a frequency-weighted extension of a recently proposed model reduction method for linear systems is presented. The method uses convex optimization and can be used both with sample data and exact models. We also obtain bounds on the frequency-weighted error. The method is combined with a rank-minimization heuristic to approximate multiinput– multi-output systems.We also present two applications— environment compensation and simplification of interconnected models — where we argue the proposed methods are useful

A novel haptic model and environment for maxillofacial surgical operation planning and manipulation

This paper presents a practical method and a new haptic model to support manipulations of bones and their segments during the planning of a surgical operation in a virtual environment using a haptic interface. To perform an effective dental surgery it is important to have all the operation related information of the patient available beforehand in order to plan the operation and avoid any complications. A haptic interface with a virtual and accurate patient model to support the planning of bone cuts is therefore critical, useful and necessary for the surgeons. The system proposed uses DICOM images taken from a digital tomography scanner and creates a mesh model of the filtered skull, from which the jaw bone can be isolated for further use. A novel solution for cutting the bones has been developed and it uses the haptic tool to determine and define the bone-cutting plane in the bone, and this new approach creates three new meshes of the original model. Using this approach the computational power is optimized and a real time feedback can be achieved during all bone manipulations. During the movement of the mesh cutting, a novel friction profile is predefined in the haptical system to simulate the force feedback feel of different densities in the bone

Robustness results in LQG based multivariable control designs

The robustness of control systems with respect to model uncertainty is considered using simple frequency domain criteria. Results are derived under a common framework in which the minimum singular value of the return difference transfer matrix is the key quantity. In particular, the LQ and LQG robustness results are discussed

DESIGN OF PMU BASED REAL TIME FUZZY LOGIC SVC DAMPING CONTROLLER TO ENHANCE INTER- AREA OSCILLATION DAMPING

Inter-area oscillation has been identified as a significant problem in the utility systems due to the damages that it may cause as well as the limitation introduced to power transfer capability. A contemporary solution to this issue is by adding power system stabilizer (PSS) to the generator's automatic voltage regulator (AVR). Although nowadays most of the generators are equipped with conventional PSSs, their effects are only noticed on the damping of local oscillations and they do not contribute effectively on damping the inter-area oscillations. Adding auxiliary signals (stabilizing signals) to Flexible AC Transmission System (FACTS) device such as Static VAr Compensator (SVC)&Static Synchronous Compensator (STATCOM) would help in extending the power transfer capability and enhancing the voltage. The stabilizing signals can be derived from damping controller. In this thesis, a Phasor Measurement Unit (PMU) based real-time, Hardware in the Loop, fuzzy logic shunt FACTS controller is proposed to ensure a satisfactory damping of inter-area oscillations which will enhance system stability and increase power transfer capability. The concerned power system has been modeled using Real-Time Digital Simulator (RTDS), where the designed Hardware-in-the-loop damping controller was tested for the sake of evaluating the effectiveness of the proposed controller in enhancing the damping of inter-area oscillations. Time-domain simulations results have shown that the designed Fuzzy damping controller enhance the damping of inter-area oscillations of interconnected power system. This study is aimed to analyze the potential applications of PMU in the interconnected power systems of GCC smart power grid. These systems are expected to face a stability problem of the inter-area mode of oscillations due to the weak tie-lines that connect the systems

RBF Neural Network of Sliding Mode Control for Time-Varying 2-DOF Parallel Manipulator System

This paper presents a radial basis function (RBF) neural network control scheme for manipulators with actuator nonlinearities. The control scheme consists of a time-varying sliding mode control (TVSMC) and an RBF neural network compensator. Since the actuator nonlinearities are usually included in the manipulator driving motor, a compensator using RBF network is proposed to estimate the actuator nonlinearities and their upper boundaries. Subsequently, an RBF neural network controller that requires neither the evaluation of off-line dynamical model nor the time-consuming training process is given. In addition, Barbalat Lemma is introduced to help prove the stability of the closed control system. Considering the SMC controller and the RBF network compensator as the whole control scheme, the closed-loop system is proved to be uniformly ultimately bounded. The whole scheme provides a general procedure to control the manipulators with actuator nonlinearities. Simulation results verify the effectiveness of the designed scheme and the theoretical discussion