Reset Control Research Articles

Reset control systems: stabilization by nearly-periodic reset

AbstractIn this paper the class of linear impulsive systems is considered. These systems are those with a continuous linear dynamics for all time, except at a sequence of instants. When such a discrete time occurs, the state undergoes a jump, or more precisely follows a discrete linear dynamics. The sequence of time instants, when a discrete dynamics occurs, is nearly-periodic only, i.e. it is distant from a periodic sequence to an uncertain distance. This paper succeeds to state tractable conditions to analyze the stability, and to design reset matrices such that the hybrid system is globally asymptotically stable to the origin. The approach is based on a polytopic embedding of the uncertain dynamics. An example illustrates the main stability result.

Quadratic Stability of Uncertain Reset Control Systems

AbstractIn this paper, we consider quadratically robust stability of reset control systems with uncertain output matrices. We show that, when the uncertain set is a convex polyhedron, the necessary and sufficient condition for a reset control system to be quadratically robustly stable is that the vertices of the uncertain set share a common block diagonal Lyapunov function.

On Reset Control Systems with Discrete-time Triggering Conditions

AbstractIn reset control systems, reset actions are triggered whenever a continuous signal crosses a hyperplane. In the computer-based implementation, however, the continuous triggering signal is sampled and the triggering condition is replaced by a discrete-time counterpart. In this work, we are interested in stability analysis and design of reset control systems based directly on discrete-time triggering conditions. First of all, a relationship between reset control systems and switched systems is established and some stability criteria are obtained. Secondly, it is revealed that a reset control system can be regarded as a hybrid system combining an underdamped baseline system and an overdamped reset mode. In addition, it is showed by example that the reset matrix, which is assumed to be zero in general, has significant effect on the damping ratio of the reset mode and thus can be adjusted to further improve the performance. Based on this observation, a three-step design procedure is proposed. A hard disk drive example is also investigated to demonstrate the proposed design procedure.

Reset Times-Dependent Stability of Reset Control Systems

Reset control systems are a special type of impulsive hybrid systems in which the time evolution depends both on continuous dynamics between resets and the discrete dynamics corresponding to the reset instants. In this work, stability of reset control systems is approached by using an equivalent (time-varying) discrete time system, introducing new sufficient stability conditions that explicitly depend on the reset times. The stability conditions overcome previous results such as the -condition and can be also applied to reset systems with unstable base system. In addition, stabilization of reset control systems is approached for systems with stable base system, resulting in that a reset control system can be always stabilized if reset intervals are forced to be large enough, avoiding resets at some crossings if necessary.

New directions on hybrid control systems

Nonlinear control systems have undergone tremendous advances in the last two decades at the levels of theory and applications. Among those, a class of particular interest is that one resulting from the interaction of a control system with a system governed by different dynamics. This class of system lies in the hybrid and nonlinear control systems field. In the last decade, the study of such hybrid systems, whose behavior can be mathematically described using a mixture of logicbased switching and difference/differential linear or nonlinear equations, has attracted important research efforts. It is motivated by the fact that many physical systems are controlled or supervised by controllers with such mixed dynamics. In many applications (such as Automotive, Networked control systems, Energy management, Biology, etc.), analysis and design methods for systems evolving both continuously and discontinuously components are then needed. Furthermore, among many important problems formulated in the context of hybrid systems, switched control systems have been attracting much attention in recent years. A switched system is a hybrid dynamical system consisting of a family of continuous time subsystems and a rule that governs the switching between them. Many important questions that relate to their behavior still remain unanswered. Some of these questions have been characterized by NP-hardness and undecidability results. Many results are relevant not only for the community working on hybrid systems but have also many consequences in linear and nonlinear control theory. This special issue takes place in the context of hybrid systems and concerns all the aspects of analysis properties or control design problems. In accordance with the context above mentioned, the objective of this special issue aims at identifying the recent advances and the associate challenging mathematical problems regarding all the aspects of analysis properties or control design issues. Hence, the special issue covers some aspects regarding: • analysis of stability of hybrid systems; • reset control systems; • systems subject to switching operators; • design of hybrid controllers for linear or nonlinear control systems; • overcoming the limitations of classical feedbacks using nonlinear or hybrid laws; • practical and implementation aspects in nonlinear and hybrid contexts; • numerical simulations of hybrid systems; • analytical tools for hybrid optimal control.

Piecewise quadratic Lyapunov functions for linear control systems with First Order Reset Elements

For a class of reset control systems, we reconsider the piecewise quadratic Lyapunov function construction proposed in Zaccarian et al. [2005]. In particular, we propose an alternative construction that addresses an analysis subtlety overlooked in that preliminary result. An example illustrates the potential pitfalls of ignoring this analysis subtlety. Another example is used to show that the new statement leads to numerical results that are similar to the ones that come from Zaccarian et al. [2005].

Limit cycles analysis of reset control systems with reset band

The reset band is a simple idea, and a must in practice, to improve reset compensation by adding extra phase lead in a feedback loop. However, a formal treatment of how the reset band can affect stability and performance of a reset control system is still an open issue. This work approaches the problem of the existence and stability of limit cycles of reset control systems with reset band. A frequency domain approach is given by using standard methods based on the describing function. In addition, closed-form expressions have been obtained for the describing function of arbitrary order full reset compensators with and without reset band.

Design and analysis of a low power passive UHF RFID transponder IC

This paper presents a low power passive UHF RFID transponder IC, which is compatible with ISO/IEC 18000-6B Standard, operating at the 915 MHz ISM band with the total supply current consumption less than 10 μA. The fully integrated passive transponder, whose reading distance more than 3 m at 4 W (36 dBm) EIRP with an antenna gain less than 1.5 dBi, is powered by the received RF energy. There are no external components, except for the antenna. The transponder IC includes matching network, rectifier, regulator, power on reset circuit, local oscillator, bandgap reference, AM demodulator, backscatter, control logic and memory. The IC is fabricated using Chartered 0.35 μm two-poly four-metal CMOS process with Schottky diodes and EEPROM supported. The die size is 1.5 mm × 1.0 mm.

Performance analysis of reset control systems

AbstractIn this paper we present a general linear matrix inequality‐based analysis method to determine the performance of a SISO reset control system in both the ℒ︁2 gain and ℋ︁2 sense. In particular, we derive convex optimization problems in terms of LMIs to compute an upperbound on the ℒ︁2 gain performance and the ℋ︁2 norm, using dissipativity theory with piecewise quadratic Lyapunov functions. The results are applicable to for all LTI plants and linear‐based reset controllers, thereby generalizing the available results in the literature. Furthermore, we provide simple though convincing examples to illustrate the accuracy of our proposed ℒ︁2 gain and ℋ︁2 norm calculations and show that, for an input constrained ℋ︁2 problem, reset control can outperform a linear controller designed by a common nonlinear optimization method. Copyright © 2009 John Wiley & Sons, Ltd.

Simulational Analysis of Adaptive Outdoor Reset Control based on a Fuzzy Target Temperature Gap for a Hydronic Radiant Floor Heating System

This paper proposes an adaptive outdoor reset control based on a fuzzy target temperature gap for a hydronic radiant floor heating system. A hydronic radiant floor heating system has nonlinear characteristics, such as the effect of time delay and temperature inertia. In hydronic radiant floor heating systems, a heating source system, such as a boiler, has a target temperature gap determined by nonlinear characteristics. An unadjusted target temperature gap causes the indoor temperature to fail at tracking the desired level, and results in many wide swings in room temperature. For these reasons, the hydronic radiant heating system has lower energy efficiency than is desired. To solve these problems, a fuzzy system is employed to find the dynamic target temperature gap of the hydronic radiant floor heating system under both indoor and outdoor temperatures. The fuzzy target gap temperature can determine calorie supply time and On-Off time. The obtained control system shows effectiveness compared with a classical On-Off controller. Simulational results are provided to illustrate the control performance.

태양광 컨버터 시스템의 과도응답 개선을 위한 비선형 적응제어 및 안정성 해석

In photovoltaic(PV) generator systems, DC-DC converters are significantly considered for control system performance in power quality point of view. This paper presents a novel adaptive control method for DC-DC converters applied in PV generator systems. First, we derive a state-space average model of the converter system and then propose a reset control methodology to enhance transient response performance for time-varying PV systems. For estimating parameters of a reset control, a gradient descent optimization is utilized and an adjustment rule of them are derived respectively. An objective of the optimization is that characteristic equation of an augmented system model which is formed with an converter system model and an reset control is to trace a predefined polynomial given as a reference characteristic model. Next, we accomplish stability analysis by means of a well-known Lyapunov theory for nonlinear converter systems including time-varying voltage excitation from a PV generator. Numerical simulation demonstrates reliability of our control methodology and its superiority by comparison to a traditional control strategy.

Delay-dependent stability of reset systems

This work presents results on the stability of time-delay systems under reset control. The case of delay-dependent stability is addressed, by developing a generalization of previous stability results for reset systems without delay, and also a generalization of the delay-independent case. The stability results are derived by using appropriate Lyapunov–Krasovskii functionals, obtaining LMI (Linear Matrix Inequality) conditions and showing connections with passivity and positive realness. The stability conditions guarantee that the reset action does not destabilize the base LTI (Linear Time Invariant) system. Several interpretations are given for these conditions in terms of impulsive control, which provide insights into the potentials of reset control.

A passivity-based approach to reset control systems stability

The stability of reset control systems has been mainly studied for the feedback interconnection of reset compensators with linear time-invariant systems. This work gives a stability analysis of reset compensators in feedback interconnection with passive nonlinear systems. The results are based on the passivity approach to L 2 -stability for feedback systems with exogenous inputs, and the fact that a reset compensator will be passive if its base compensator is passive. Several examples of full and partial reset compensations are analyzed, and a detailed case study of an in-line pH control system is given.

Discrete-Time Optimal Reset Control for Hard Disk Drive Servo Systems

This paper proposes a design method of discrete-time optimal reset control with the reset time instants prespecified. With a base linear system designed conventionally, the discrete-time reset law design aims at improving the system transient responses. The design method can guarantee system stability, and the controller is obtained by solving Riccati equations. The proposed design method is applied to short-span and long-span track seeking of a hard disk drive servo system. Experimental results show that the proposed design is much more capable of improving transient response than traditional control design methods.

네트워크 기반 시간지연 시스템을 위한 리세트 제어 및 확률론적 예측기법을 이용한 온라인 학습제어시스템

This paper presents a novel control methodology for communication network based nonlinear systems with time delay nature. We construct a nominal nonlinear control law for representing a linear model and a reset control system which is aimed for corrective control strategy to compensate system error due to uncertain time delay through wireless communication network. Next, online neural control approach is proposed for overcoming nonstationary statistical nature in the network topology. Additionally, DBN (Dynamic Bayesian Network) technique is accomplished for modeling of its dynamics in terms of casuality, which is then utilized for estimating prediction of system output. We evaluate superiority and reliability of the proposed control approach through numerical simulation example in which a nonlinear inverted pendulum model is employed as a networked control system.

Modelica-based modelling and simulation to support research and development in building energy and control systems

Traditional building simulation programs possess attributes that make them difficult to use for the design and analysis of building energy and control systems and for the support of model-based research and development of systems that may not already be implemented in these programs. This article presents characteristic features of such applications, and it shows how equation-based object-oriented modelling can meet requirements that arise in such applications. Next, the implementation of an open-source component model library for building energy systems is presented. The library has been developed using the equation-based object-oriented Modelica modelling language. Technical challenges of modelling and simulating such systems are discussed. Research needs are presented to make this technology accessible to user groups that have more stringent requirements with respect to the numerical robustness of simulation than a research community may have. Two examples are presented in which models from the here described library were used. The first example describes the design of a controller for a nonlinear model of a heating coil using model reduction and frequency domain analysis. The second example describes the tuning of control parameters for a static pressure reset controller of a variable air volume flow system. The tuning has been done by solving a non-convex optimization problem that minimizes fan energy subject to state constraints.

Delay-Independent Stability of Reset Systems

Reset control systems have potential advantages to overcome fundamental limitations of LTI compensation. However, since a reset compensator may destabilize a stable base LTI system, stability needs to be guaranteed in advance for a proper practical application of reset control. This works extends previous stability results of reset control systems to consider the case of LTI plants with time-delays. Stability independent of the delay criteria are developed both by means of LMIs and in the frequency domain by using the KYP Lemma.

Stability Analysis of reset control systems with reset band

Abstract Reset band is a simple idea, and a must in practice, to improve reset compensation by adding extra phase lead in a feedback loop. However, a formal treatment of how the reset band can affect stability and performance of a reset control system is still an open issue. This work approaches the problem of existence and stability of limit cycles of reset control systems with reset band. A frequency domain approach is given by using standard methods based on the describing function. In addition, closed-form expressions have been obtained for the describing funtion of arbitrary order full reset compensators with and without reset band.

Stability analysis and design of reset systems: Theory and an application

This paper investigates stability analysis and design of reset control systems where the reset time instants are pre-specified. Firstly, in order to quantify stability of reset control systems, we propose an approach which does not rely on the stability of base linear systems. Based on this, some Lie-algebraic conditions for stability of reset control systems are obtained. Then, we develop a method for reset law design which aims at improving transient responses of the base linear systems. In addition, observer-based design is also considered. We prove that under some mild conditions, reset controller and observer can be designed separately. The obtained results are applied to short-span-seeking control of a kind of single stage hard disk drive servo systems. Simulations show that the proposed design is much more capable of improving transient response than traditional control design techniques.

Development of an extended reset controller and its experimental demonstration

Reset control aims at enhanced performance that cannot be obtained by linear controllers. The conventional reset control is simple for implementation by resetting some of its controller states to zero when its input meets a threshold. However, it is found that in some cases the enhanced performance of conventional reset control is still limited such as with only partial reduction of the overshoot in a step reference response. Thus, the stability analysis and design of the reset control system are extended, where the reset time instances are prespecified and the controller states are reset to certain non-zero values, which are calculated online in terms of the system states for optimal performance. Experimental results on a piezoelectric positioning stage demonstrate that the extended reset control can further reduce the overshoot and thus achieve shorter settling time than the conventional reset control. Moreover, robustness tests against various step levels, disturbance and sensor noise are presented.