Синтез и исследование работы позиционной системы с линей-ным актуатором

The paper considers a positional system with a linear actuator and modal control. The use of the software extensions of the MATLAB‘s Control System Toolbox enabled a synthesis of the factors of the modal regulator for different types of the characteristic polynomials of the closed-loop system. Dynamic characteristics of the obtained system with different factors of the modal controller were estimated in by means of a mathematical model of the studied actuator in the Simulink application. The resulting structure and method of synthesis of a control system with the linear solenoid actuator provide an aperiodic nature of transient process of the working gear travel. This enables small displacements of various objects at uncertain parameters of power circuits and loads with a fast response time and minimal static error.Рассмотрена позиционная система с линейным соленоидным актуатором и модальным управлением. Для придания системе инвариантных свойств в переходных режимах работы при неопределенности параметров силовой схемы и нагрузки с помощью программного расширения Control System Toolbox пакета MATLAB осуществлен синтез коэффициентов модального регулятора при различных видах ха-рактеристических полиномов замкнутой системы. Оценка показателей качества динамических харак-теристик полученной системы с различными коэффициентами модального регулятора выполнена путем математического моделирования режимов работы исследуемого электропривода в приложении Simulink. Полученные структура и методика синтеза системы управления с линейным соленоидным актуатором обеспечивают апериодический характер переходного процесса передвижения рабочего механизма. Это дает возможность осуществлять малые перемещения различных объектов при неопределенности параметров силовых схем и нагрузки с высоким быстродействием и минимальной статической ошибкой

POLYNOMIAL STATIC OUTPUT FEEDBACK H ∞ CONTROL FOR CONTINUOUS-TIME LINEAR SYSTEMS VIA DESCRIPTOR APPROACH

International audienceThis paper deals with the problem of the robust static output feedback H ∞ control (SOFC) for continuous linear systems with polytopic uncertainties. The controller has been gotten by the use of descriptor redundancy. Under this approach a sufficient condition is provided for the existence of a solution to the problem. Thus, the advantage of this method is to obtain more free matrices in the design condition, also the polynomial approach helps to have a less conservative result. In the end, the performance of the method is shown by several examples

Fixed-order Controller Design of Linear Systems

The problem of fixed-order dynamic output feedback control of systems subject to polytopic uncertainties is a challenging issue in the community of robust control theory. Various LMI-based methods have been developed since the last decade. In this report, we show that most of slack-matrix based methods in the literature implicitly/explicitly rely on the concept of Strictly Positive Realness (SPRness) of transfer functions presented by KYP Lemma. In fact

Optimal control of dynamical systems with time-invariant probabilistic parametric uncertainties

Thesis: Ph. D., Massachusetts Institute of Technology, Department of Chemical Engineering, February 2018.Cataloged from PDF version of thesis. "September 2017." Handwritten on title page "February 2018."Includes bibliographical references (pages 117-121).The importance of taking model uncertainties into account during controller design is well established. Although this theory is well developed and quite mature, the worst-case uncertainty descriptions assumed in robust control formulations are incompatible with the uncertainty descriptions generated by commercial model identification software that produces time-invariant parameter uncertainties typically in the form of probability distribution functions. This doctoral thesis derives rigorous theory and algorithms for the optimal control of dynamical systems with time-invariant probabilistic uncertainties. The main contribution of this thesis is new feedback control design algorithms for linear time-invariant systems with time-invariant probabilistic parametric uncertainties and stochastic noise. The originally stochastic system of equations is transformed into an equivalent deterministic system of equations using polynomial chaos (PC) theory. In addition, the H2- and H[infinity symbol]-norms commonly used to describe the effect of stochastic noise on output are transformed such that the eventual closed-loop performance is insensitive to parametric uncertainties. A robustifying constant is used to enforce the closed-loop stability of the original system of equations. This approach results in the first PC-based feedback control algorithm with proven closed-loop stability, and the first PC-based feedback control formulation that is applicable to the design of fixed-order state and output feedback control designs. The numerical algorithm for the control design is formulated as optimization over bilinear matrix inequality (BMI) constraints, for which commercial software is available. The effectiveness of the approach is demonstrated in two case studies that include a continuous pharmaceutical manufacturing process. In addition to model uncertainties, chemical processes must operate within constraints, such as upper and lower bounds on the magnitude and rate of change of manipulated and/or output variables. The thesis also demonstrates an optimal feedback control formulation that explicitly addresses both constraints and time-invariant probabilistic parameter uncertainties for linear time-invariant systems. The H2-optimal feedback controllers designed using the BMI formulations are incorporated into a fast PC-based model predictive control (MPC) formulation. A numerical case study demonstrates the improved constraint satisfaction compared to past polynomial chaos-based formulations for model predictive control.by Dongying Erin Shen.Ph. D

Optimal Output Modification and Robust Control Using Minimum Gain and the Large Gain Theorem

When confronted with a control problem, the input-output properties of the system to be controlled play an important role in determining strategies that can or should be applied, as well as the achievable closed-loop performance. Optimal output modification is a process in which the system output is modified in such a manner that the modified system has a desired input-output property and the modified output is as similar as possible to a specified desired output. The first part of this dissertation develops linear matrix inequality (LMI)-based optimal output modification techniques to render a linear time-invariant (LTI) system minimum phase using parallel feedforward control or strictly positive real by linearly interpolating sensor measurements. H-ininifty-optimal parallel feedforward controller synthesis methods that rely on the input-output system property of minimum gain are derived and tested on a numerical example. The H2- and H-infinity-optimal sensor interpolation techniques are implemented in numerical simulations of noncolocated elastic mechanical systems. All mathematical models of physical systems are, to some degree, uncertain. Robust control can provide a guarantee of closed-loop stability and/or performance of a system subject to uncertainty, and is often performed using the well-known Small Gain Theorem. The second part of this dissertation introduces the lessor-known Large Gain Theorem and establishes its use for robust control. A proof of the Large Gain Theorem for LTI systems using the familiar Nyquist stability criterion is derived, with the goal of drawing parallels to the Small Gain Theorem and increasing the understanding and appreciation of this theorem within the control systems community. LMI-based robust controller synthesis methods using the Large Gain Theorem are presented and tested numerically on a robust control benchmark problem with a comparison to H-infinity robust control. The numerical results demonstrate the practicality of performing robust control with the Large Gain Theorem, including its ability to guarantee an uncertain closed-loop system is minimum phase, which is a robust performance problem that previous robust control techniques could not solve.PHDAerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/143934/1/caverly_1.pd

Fixed-structure Control of LTI Systems with Polytopic-type Uncertainty:Application to Inverter-interfaced Microgrids

This thesis focuses on the development of robust control solutions for linear time-invariant interconnected systems affected by polytopic-type uncertainty. The main issues involved in the control of such systems, e.g. sensor and actuator placement, control configuration selection, and robust fixed-structure control design are included. The problem of fixed-structure control is intrinsically nonconvex and hence computationally intractable. Nevertheless, the problem has attracted considerable attention due to the great importance of fixed-structure controllers in practice. In this thesis, necessary and sufficient conditions for fixed-structure H_inf control of polytopic systems with a single uncertain parameter in terms of a finite number of bilinear matrix inequalities (BMIs) are developed. Increasing the number of uncertain parameters leads to sufficient BMI conditions, where the number of decision variables grows polynomially. Convex approximations of robust fixed-order and fixed-structure controller design which rely on the concept of strictly positive realness (SPRness) of transfer functions in state space setting are presented. Such approximations are based on the use of slack matrices whose duty is to decouple the product of unknown matrices. Several algorithms for determination and update of the slack matrices are given. It is shown that the problem of sensor and actuator placement in the polytopic interconnected systems can be formulated as an optimization problem by minimizing cardinality of some pattern matrices, while satisfying a guaranteed level of H_inf performance. The control configuration design is achieved by solving a convex optimization problem whose solution delivers a trade-off curve that starts with a centralized controller and ends with a decentralized or a distributed controller. The proposed approaches are applied to inverter-interfaced microgrids which consist of distributed generation (DG) units. To this end, two important control problems associated with the microgrids are considered: (i) Current control of grid-connected voltage-source converters with L/LCL filters and (ii) Voltage control of islanded microgrids. The proposed control strategies are able to independently regulate the direct and quadrature (dq) components of the converter currents and voltages at the point of common couplings (PCC) in a fully decoupled manner and provide satisfactory dynamic responses. The important problem of plug-and-play (PnP) capability of DGs in the microgrids is also studied. It is shown that an inverter-interfaced microgrid consisting of multi DGs under PnP functionality can be cast as a system with polytopic-type uncertainty. By virtue of this novel description and use of the results from theory of robust control, the stability of the microgrid system under PnP operation of DGs is preserved. Extensive case studies, based on time-domain simulations in MATLAB/SimPowerSystems Toolbox, are carried out to evaluate the performance of the proposed controllers under various test scenarios, e.g., load change, voltage and current tracking. Real-time hardware-in-the-loop case studies, using RT-LAB real-time platform of OPAL-RT Technologies, are also conducted to validate the performance of the designed controllers and demonstrate their insensitivity to hardware implementation issues, e.g., noise and PWM non-idealities. The simulation and experimental results demonstrate satisfactory performance of the designed controllers