Design Of Linear Control Systems Research Articles

Reachable Set Estimation and Controller Design for Linear Time-Delayed Control System with Disturbances

This paper investigates reachable set estimation and state-feedback controller design for linear time-delay control systems with bounded disturbances. By constructing an appropriate Lyapunov–Krasovskii functional, we obtain a delay-dependent condition, which determines the admissible bounding ellipsoid for the reachable set of the system we considered. Then, a sufficient condition in the form of liner matrix inequalities is given to solve the problem of controller design and reachable set estimation. Then, by minimizing the volume of the ellipsoid and solving the liner matrix inequality, we obtain the desired ellipsoid and controller gain. A comparative numerical example is given to show the effectiveness of our result.

Control Design for Linear Systems With Asymmetric Input Backlash and Dead-Zone Through LMI Conditions

Control Design for Linear Systems With Asymmetric Input Backlash and Dead-Zone Through LMI Conditions

Optimal non-fragile control design for linear systems under amplitude and rate saturation: An LMI approach

In this paper, the problem of optimal non-fragile guaranteed cost control design for linear systems subject to input amplitude and rate saturation is addressed. Sufficient conditions for the existence of a non-fragile state feedback are obtained by Lyapunov stability theory. The designed controller not only guarantees the asymptotic stability of the overall closed-loop system with a minimum upper bound of a cost function, but also ensures the actuator saturation avoidance. This problem is transformed into an optimization problem with linear matrix inequality (LMI) constraints. The proposed method guarantees that the control input amplitude and rate remain within the allowable ranges and do not exceed the considered bounds. The simulation results illustrate the effectiveness and superiority of the proposed theoretical results.

Design of Multivariate PID Controller for Power Networks Using GEA and PSO

The issue of proper modeling and control for industrial systems is one of the challenging issues in the industry. In addition, in recent years, PID controller design for linear systems has been widely considered. The topic discussed in some of the articles is mostly speed control in the field of electric machines, where various algorithms have been used to optimize the considered controller, and always one of the most important challenges in this field is designing a controller with a high degree of freedom. In these researches, the focus is more on searching for an algorithm with more optimal results than others in order to estimate the parameters in a more appropriate way. There are many techniques for designing a PID controller. Among these methods, meta-innovative methods have been widely studied. In addition, the effectiveness of these methods in controlling systems has been proven. In this paper, a new method for grid control is discussed. In this method, the PID controller is used to control the power systems, which can be controlled more effectively, so that this controller has four parameters, and to determine these parameters, the optimization method and evolutionary algorithms of genetics (EGA) and PSO are used. One of the most important advantages of these algorithms is their high speed and accuracy. In this article, these algorithms have been tested on a single-machine system, so that the single-machine system model is presented first, then the PID controller components will be examined. In the following, according to the transformation function matrix and the relative gain matrix, suitable inputs for each of the outputs are determined. At the end, an algorithm for designing PID controller for multivariable MIMO systems is presented. To show the effectiveness of the proposed controller, a simulation was performed in the MATLAB environment and the results of the simulations show the effectiveness of the proposed controller.

Quantized Control Design for Linear Systems Using Reinforcement Learning

In this paper, a quadratic stabilizing controller minimizing a cost function is designed through model-free and online reinforcement learning for systems with logarithmic quantized input. By introducing a new gain dependent on quantization density, the input and related weighting matrix in the cost function are deviated from their original ones. Then, using these deviated parameters, the controller is trained through reinforcement learning such that the closed-loop system satisfies the quadratic stability condition with the cost function minimized. An inverted pendulum example is used to show the effectiveness and merits of the proposed method.

Advanced controller design for uncertain linear systems with time‐varying delays via augmented zero equality approach

This paper deals with the stability analysis and controller design for linear systems with time‐varying delays and parameter uncertainties. By choosing appropriate augmented Lyapunov–Krasovskii functionals, a set of linear matrix inequalities is derived to get advanced feasible region of stability and controller gain matrices that guarantee the asymptotic stability of the concerned systems within maximum bound of time delays and its time derivative. To further reduce the conservatism of stabilization criterion, a recently developed mathematical technique that constructed a new augmented zero equality is applied. Finally, two numerical examples are utilized to show the validity and superiority of the proposed methods.

Design of Saturating State Feedback With Sign-Indefinite Quadratic Forms

In this article, we propose a novel class of piecewise smooth Lyapunov functions leading to linear-matrix-inequality-based stability/performance analysis and control design for linear systems with saturating inputs. We provide conditions for global properties, and also conditions for local properties and guaranteed estimates of the basin of attraction. The backbone of our result consists in using quadratic forms with constant matrices that are not necessarily sign definite, thereby providing additional degrees of freedom. Using generalized sector conditions involving the dead-zone nonlinearity and its derivative, we formulate convex optimization conditions to verify their positivity in the region of interest. Several numerical examples with connections to existing results illustrate the potential behind our novel construction.

A GEVP formulation for robust predictor feedback controller design of linear systems with uncertain input delay

Predictor feedback controllers are irreplaceable and widely used for systems with long input delays. However, it is also known to be sensitive to mismatch between the nominal input delay and the true unknown one. In this paper, we propose a robust predictor feedback controller design to enlarge the admissible delay mismatch, while keeping the convergence rate within a prescribed level. It is shown that the controller synthesis problem can be cast into a generalised eigenvalue problem (GEVP).

Event-triggered controller design for linear systems with saturated input and bounded disturbance

This paper deals with the stabilisation problem of linear systems subject to saturated input and bounded disturbance via event-triggered control strategy. In a hybrid systems framework, both a state feedback law and a static output feedback law are proposed to design the event-triggered controllers, which provide solutions to the event-triggered control collaborative design problem. For the case of using static output feedback, an iterative linear matrix inequality algorithm is proposed to obtain the feedback gain. In addition, the local uniform ultimate boundedness of the closed-loop system is ensured. Finally, two examples are given to illustrate the effectiveness of the proposed controllers.

Regional stabilization and H∞ congestion control with input saturation

Designing robust active queue management subjected to network imperfections is a challenging problem. Motivated by this topic, we addressed the problem of controller design for linear systems with variable delay and unsymmetrical constraints by the scaled small gain theorem. We designed two mechanisms: robust enhanced proportional derivative; and robust enhanced proportional derivative subjected to input saturation. Discussion of their practical implementations along with extensive comparisons by MATLAB and NS3 illustrate the improved performance and the enlargement of the domain of attraction regarding some literature results.

Approximate optimal synthesis of operational control systems for dynamic objects based on quasilinearization and sufficient optimality conditions

A new approach to the analytical design of linear and nonlinear integrated automatic control systems (ACS) of a real (accelerated) time scale, based on the joint use of dynamic programming technologies and the quasilinearization method, is presented. For continuous dynamic systems, the foundations of the theory of nonlinear synthesis in a degenerate (synergetic) formulation are given.

Implementation of Stir-Speed Adopted Controllers Onto a Batch Bioreactor for Improved Fermentation

Quality, quantity, and economy of the fermentation product depend on the transient response and the steady-state of the fermentation process. Due to its simple construction, an industrial batch bioreactor cannot be equipped with a closed-loop control system that applies adding or removing substances during fermentation. This theoretical and practical study displays how fermentation can be controlled, in this case by altering the rotational speed of a stirrer system of such a bioreactor. A numerical analysis was employed to set up a mathematical model that describes the impact of the stirrer speed on the fermentation. The model consists of linear and non-linear parts. To determine their parameters, a least square identification and a particle swarm optimization method were utilized. The model was fitted and tested experimentally in a laboratory on the operating batch bioreactor. The design and synthesis of a conventional linear control system and an advanced model reference adaptive control system, which is also convenient for control of non-linear controlled plants, were carried out based on the determined mathematical model. Both control concepts were first implemented into the dSpace 1103 control system, convenient for faster development and prototyping. Finally, they were realized with the Siemens SIMATIC S7 programmable logic controller, which was ideal for industrial environment operation. During the operation of the bioreactor, the control systems were tested along with the acquisition of measured data involving CO2 concentration of a fermentation product. The findings of successfully applying linear and adaptive controllers of the milk fermentation in the batch bioreactor are analyzed and presented.

Lyapunov Redesign for Input and State Delays Systems by Using Optimal Predictive Control and Ultimate Bound Approaches: Theory and Experiments

This article deals with the robust control design for linear systems with input and state delays, subject to nonvanishing matched disturbances. The controller is synthesized with the Lyapunov redesign technique in two stages: first, an optimal predictor compensates the input delay of the nominal system while a quadratic performance index is minimized. Then, the robust component guarantees that the solutions are ultimately bounded. The theoretical results are experimentally validated through a dehydration process, with the controller digital implementation on an industrial programmable automation controller cDAQ-9132.

Compensator Design for Non-autonomous Linear Control Systems

Compensator Design for Non-autonomous Linear Control Systems

Adaptive sliding mode observer–based decentralized control design for linear systems with unknown interconnections

In this study, a class of linear interconnected systems with unknown interconnections between subsystems is considered. Primarily, an observer is designed to reconstruct an equivalent of unknown interconnections that are considered uncertain. A decentralized controller will be thereafter designed to keep the stability of the original system when the estimated system is at risk of instability due to the lack of information on interconnections. To design a decentralized observer and to estimate states of each subsystem, without knowing the relations between subsystems, a combination of Luenberger observer along with the adaptive sliding mode technique is used. Because the interconnected system might generally be unstable, a state feedback controller is used to stabilize each subsystem using estimated states together with the output of other subsystems. The stability of the system and the convergence of the discrepancy between real states and that of estimated are guaranteed, gaining the Lyapunov theory. Simulation results signify that the proposed decentralized controller based on a new adaptive sliding mode observer is highly efficient for linear interconnected systems with unknown interconnections.

Extracting counterexamples induced by safety violation in linear hybrid systems

Control design for linear systems typically involves pole placement and computing Lyapunov functions. While these tools are useful for ensuring stability, they are not always helpful in ensuring safety. Control designers can employ model checking as a tool for checking safety. We believe that supplementing the model checker to provide various types of counterexamples for the safety specification would help the control designer in the control development process. In this paper, we describe a technique for obtaining the variety of counterexamples for a safety violation in linear hybrid systems. More specifically, we develop algorithms to extract the longest counterexample — the execution that stays in the unsafe set for the longest contiguous time, deepest counterexample — the execution that ventures the most into the unsafe set in a user specified direction, and the robust counterexample — the unsafe execution from which some bounded perturbation yields a new counterexample. These measures for classifying counterexamples can further assist in quantifying controllers’ performance.

Metzler matrix-based switching control scheme for linear systems with prescribed performance guarantees

This paper investigates the issue of control design for linear systems with prescribed performance. The novelty of the proposed solution relies on a switching control scheme that uses the interval theory. Different from the existing prescribed performance control approaches, the error transformation and the logarithmic/tangent function are no longer required in the presented control. Alternatively, a switching scheme inspired by the interval observer technique is introduced to ensure the errors not violating performance bound functions. The proposed control establishes an unified prescribed performance control framework which covers the bounded stability, asymptotic stability and finite-time stability only via selecting the corresponding performance bound functions. Numerical examples are simulated to demonstrate the effectiveness of the proposed approach.

An interactive teaching/learning approach to the design of robust linear control systems using the closed-loop shaping methodology

Usually the controller is designed working on the open-loop transfer function. However, it is also possible to design the controller working on the closed-loop transfer functions. The closed-loop shaping methodology offers a straightforward framework which allows designers and students to focus on the required specification fulfillment and dealing with inherent linear systems limitations without complex computations or using difficult algorithms. This article summarizes the basic ideas of the manual closed-loop shaping methodology, and its application to the design of robust controllers for uncertainty linear systems. An interactive software tool for learning/teaching this methodology is also presented.

Closed-Loop Shaping Linear Control System Design: An Interactive Teaching/Learning Approach [Focus on Education

The frequency domain is one of the most popular and powerful frameworks for designing control systems. Usually, the controller is designed by working on the openloop transfer function. However, it is also possible to design the controller by working on the closed-loop transfer functions. This closed-loop shaping methodology offers a straightforward framework that enables designers and students to focus on fulfilling the required specifications and dealing with inherent linear systems limitations without the need for complex computations or the use of difficult algorithms. In comparison to open-loop shaping, closed-loop shaping offers an exact approach in a very simple framework. Interactive software tools have proven to be particularly useful techniques with high impact on control education. This kind of interactive tool has been demonstrated to help students learn in a much more active way. This article summarizes the basic ideas of manual closed-loop shaping and presents the basic functionality of the Interactive Tool for Closed-Loop Shaping Control Design (ITCLSD). Different illustrative examples are included to show the uses of the ITCLSD.

Towards Design of Quasilinear Gurvits Control Systems

The design problem of control systems for nonlinear plants with differentiated nonlinearity is considered. The urgency of this problem is caused by the big difficulties of practical design of nonlinear control systems with the help of the majority of known methods. In many cases, even provision by these methods of just stability of equilibrium point of a designing system represents a big challenge. Distinctive feature of the method of nonlinear control systems design considered below is the use of the nonlinear plants models represented in a quasilinear form. This form of the nonlinear differential equations exists, if nonlinearities in their right parts are differentiated across all arguments. The quasilinear model of the controlled plant allows reducing the design problem to the solution of an algebraic equations system, which has the unique solution if the plant is controlled according to the controllability condition provided in the article. This condition is similar to the controllability condition of the Kalman’s criterion. Procedure of the nonlinear control systems design on a basis of the plant’s quasilinear models is very simple. Practically, it is close to the known polynomial method of the linear control systems design. The equations of the nonlinear systems designed with application of the plant’s quasilinear models also can be represented in the quasilinear form.
 The basic result of this article is the proof of the theorem and the corollary from it about conditions of the asymptotical stability at whole of the equilibrium point of the nonlinear control systems designed on a basis of the plant’s quasilinear models. For the proof of the theorem and consequence, the properties of simple matrixes and known theorems of stability of the indignant systems of the differential equations are used. A way of the stability research of the equilibrium point of the quasilinear control systems based on the proved theorem is illustrated by numerical examples. Computer simulation of these systems verifies correctness of the hypoyhesis of the proved theorem.
 Obtained results allow applying the method of nonlinear systems design on a basis of the quasilinear models for creation of various control systems for plants in power, aviation, space, robotechnical and other industries.