Digital Redesign Technique Research Articles

An Intelligent Digital Redesign Approach to the Sampled-Data Fuzzy Observer Design

Based on the intelligent digital redesign (IDR) technique, this article proposes a novel method for designing a sampled-data fuzzy observer estimating a state vector of a nonlinear oscillating system. The proposed method guarantees not only the state estimation performance but also the state matching performance of the designed sampled-data fuzzy observer. The state matching aims at making the difference between the state trajectories of a redesigned sampled-data fuzzy observer and the given continuous-time fuzzy observer small enough. Thus, it is assumed that the continuous-time fuzzy observer was appropriately designed in advance. To solve the IDR problem, we propose the linear-matrix-inequality-based design condition that simultaneously guarantees both the state estimation performance and the state matching performance. In addition, the conservativeness of the design condition is relaxed by developing a novel integral inequality condition and a fuzzified time-dependent Lyapunov–Krasovskii functional. Finally, the superiority of the proposed methodology is demonstrated by showing the state estimation performance and the state matching performance.

Plant-Input-Mapping Discretization Method for a Feedback System in the State-Space Form

AbstractThe paper proposes the digital redesign technique called plant-input-mapping (PIM) method for a feedback system described in the state-space form. The PIM method, which was originally presented in the transfer function form, focuses on the plant input signal via the plant input transfer function (PITF) and discretizes it so as to satisfy the control zero principle in the resulting discrete-time closed-loop system, which leads to guaranteeing the closed-loop stability for any nonpathological sampling interval. In accordance with this approach, the proposed PIM method focuses on the control zeros included in the plant input signal. The paper proves that the matched-pole-zero discrete-time model of the plant input state-equation (PISE) satisfies the control zero principle with the step-invariant model of the plant. Then, when the matched-pole-zero model is set as the target of model matching, the parameters of the state-space PIM controller employing the observer-based dynamic state-feedback can systematically be determined from the underlying continuous-time closed-loop system with guaranteed stability. This discretization process can immediately be applied to a state-feedback system and a class of multi-input multi-output systems without any modification, which cannot be discretized by the conventional PIM methods. The discretization performance of the proposed PIM method is evaluated through illustrative examples with comparable digital redesign methods, which reveal that the proposed method performs a good reproduction of the characteristics of the underlying closed-loop system.

Sampled-data control of underwater gliders: digital redesign approach

This paper discusses a sampled-data control problem for a nonlinear underwater glider based on the digital redesign (DR) technique. An analog controller is pre-designed based on the fully feedback-linearised model. The condition for the DR problem is proposed in terms of linear matrix inequality, using the delta-operator discrete-time models. We show that the DRed sampled-data controller guarantees the semiglobal practical asymptotic stability of the nonlinear steady gliding motion in the sampling period. The numerical simulations demonstrate the advantage of the developed methodology in terms of the larger sampling period and the better preservation of the original analog control performance than the conventional emulation technique.

Intelligent digital redesign for T–S fuzzy systems: sampled‐data filter approach

This study proposes an intelligent digital redesign (IDR) technique for sampled-data fuzzy filters of non-linear systems. The technique constructs a closed-loop system with predesigned continuous-time and sampled-data filters based on the Takagi–Sugeno (T–S) fuzzy model. The closed-loop systems ensure asymptotic stability and state-matching condition in the IDR problem. Unlike previous techniques, the proposed method solves the IDR problem without a discretization process which degrades the IDR performance. Sufficient conditions for solving the IDR problem are proposed and derived in terms of linear matrix inequalities. In addition, the performance recovery of the sampled-data fuzzy filter is shown. Finally, the feasibility of the proposed technique is demonstrated in two simulation examples.

Intelligent Digital Redesign for Sampled-data Fuzzy Control Systems Based on State-matching Error Cost Function Approach

This paper presents a novel intelligent digital redesign (IDR) technique for a sampled-data fuzzy controller of fuzzy systems which can be modeled in Takagi-Sugeno (T-S) fuzzy systems. The IDR technique, which is one of sampled-data fuzzy controller design techniques, is to effectively convert a well-designed analog fuzzy controller into a sampled-data fuzzy controller in the state-matching sense. In this paper, unlike previous IDR techniques, the state-matching error is minimized by defining the state-matching error cost function. Also, to improve the state-matching condition, the exact discretized model is used for the proposed IDR technique. The sufficient condition of the proposed IDR technique is developed and derived in terms of linear matrix inequalities (LMIs). Finally, some numerical examples are provided to verify the effectiveness of the proposed techniques.

Sampled‐data control of fuzzy systems based on the intelligent digital redesign method via an improved fuzzy Lyapunov functional approach

This study presents a linear matrix inequality (LMI) approach to the sampled-data control of Takagi-Sugeno fuzzy systems, based on the intelligent digital redesign (IDR) technique. The objective of the IDR is to design a digital control system whose trajectory closely matches that of a given well-constructed analogue control system by minimising the state-matching error. In this study, state-matching performance is enhanced by using a continuous-time state-matching criterion, which guarantees that the state-matching error is minimised through the entire time interval. Unlike previous studies, mismatched information of membership functions for both analogue and digital control systems is directly manipulated. Moreover, the authors introduce an improved fuzzy Lyapunov functional that consists of both membership functions for analogue and digital control systems, which relaxes the conservativeness of LMI conditions. Finally, two examples demonstrating the effectiveness of the authors' method are provided.

An improved digital redesign for sampled-data fuzzy control systems: Fuzzy Lyapunov function approach

This paper proposes an improved digital redesign (DR) technique for sampled-data fuzzy controllers in nonlinear systems, based on a Takagi–Sugeno (T–S) fuzzy model. To improve the performance of the DR technique, two methodologies are used: a state-matching error cost function, and a continuous-time fuzzy Lyapunov function. Using these two methodologies, a novel DR technique is proposed to guarantee both the stability and state-matching conditions of the sampled-data fuzzy control system. Further, the proposed DR technique is represented as an optimal problem using the linear matrix inequality (LMI) format. Finally, some simulation examples are provided to verify the effectiveness of the proposed technique in comparison with previous techniques.

Fuzzy filter for nonlinear sampled-data systems: Intelligent digital redesign approach

This paper presents a fuzzy filter design method for nonlinear sampled-data systems using an intelligent digital redesign (IDR) technique. Based on a Takagi–Sugeno (T–S) fuzzy model, discretized closed-loop systems with pre-designed analog fuzzy and digital fuzzy filters are presented. An IDR problem is given to guarantee both state-matching condition and asymptotic stability. Sufficient conditions for solving the IDR problem are proposed and are derived in terms of linear matrix inequalities (LMIs). Finally, a simulation example is given to show the effectiveness of the proposed method.

Intelligent digital redesign of fuzzy controller for non‐linear systems with packet losses

In this study, a novel intelligent digital redesign (IDR) technique is proposed for the sampled-data fuzzy controller of the non-linear system with packet losses. For the IDR development, the non-linear system is represented in the Takagi–Sugeno fuzzy model and the packet loss is assumed to be an independent, identically distributed Bernoulli random process. After introducing the traditional IDR technique, the closed-loop system with state-matching error and the state-matching error cost function are achieved for the development of the novel IDR technique. In the discrete-time Lyapunov sense, the exponential mean-square stability is guaranteed while minimising the state-matching error, and its sufficient condition is derived into linear matrix inequalities. Two examples are provided to verify the effectiveness of the proposed technique by comparison.

Stabilization of Controller-Driven Nonuniformly Sampled Systems via Digital Redesign

This paper deals with the stabilization problem of nonuniformly sampled systems, assuming that the controller/scheduler can select the sampling period. In this setting, we proposed a sampling-period-varying state feedback controller that stabilizes the closed-loop system for arbitrary selection of bounded sampling periods. The proposed controller is based on the digital redesign technique, which also makes the closed-loop sampled system state response close to a pre-selected closed-loop continuous system.

Intelligent digital redesign for non‐linear systems: observer‐based sampled‐data fuzzy control approach

In this study, an intelligent digital redesign (IDR) technique is proposed for an observer-based sampled-data fuzzy controller of non-linear systems. By using a Takagi–Sugeno fuzzy model, the pre-designed analog and sampled-data fuzzy controllers are supposed, and these discretised closed-loop systems are obtained, respectively. Based on the IDR problem, the authors guarantee both stability and state-matching conditions. Unlike the previous techniques, the proposed IDR not only improves the state-matching performance using the state-matching error cost function, but is also derived in the strict linear matrix inequality format. In a numerical example, the effectiveness of the proposed technique and the results of the improved performance are shown.

Decentralised control for large-scale sampled-data systems: digital redesign approach

In this paper, digital redesign (DR) techniques are presented for a decentralised controller of large-scale sampled-data systems. To improve the performance of the previous DR technique, the state-matching error is defined and directly minimised by using the state-matching error cost function. Also, the discretisation error of the interconnection term is eliminated through an exact discrete-time design approach. Sufficient conditions of the proposed DR techniques are obtained in the Lyapunov sense and are converted into optimal problems with linear matrix inequalities. Finally, two numerical examples are provided to demonstrate the performance improvement of the proposed techniques.

Intelligent digital redesign for nonlinear systems using a guaranteed cost control method

In this paper, a novel intelligent digital redesign (IDR) technique using the guaranteed cost control method is proposed for nonlinear systems which can be represented by a Takagi-Sugeno (T-S) fuzzy model. The IDR technique, which is one of the sampled-data fuzzy controller design methods, guarantees not only the stability condition of the sampled-data closed-loop system with the sampleddata fuzzy controller and the state-matching error is presented. By using the concept of the guaranteed cost control method, sufficient conditions are obtained for both minimization of the state-matching error and stabilization of the sampled-data closed-loop system and derived in terms of linear matrix inequalities (LMIs). Finally, a numerical example is provided to verify the effectiveness of the proposed technique.

Digital design of a power system stabilizer for a power system based on plant input mapping

This paper is concerned with the plant modeling for the digital redesign of a continuous-time power system stabilizer PSS for a single machine power system using Plant-Input-Mapping PIM method. The traditional approach has been to use the bilinear transform (Tustin’s method), but this needs small sampling intervals which gives some difficulties with modern control. The presented technique guarantees the stability for any sampling rate as well as it takes closed-loop characteristics into consideration. The proposed technique is successfully applied to the discretization of the conventional continuous time PSS for single-machine power system. For comparison studies the proposed technique is compared with conventional continuous-time PSS and Tustin’s PSS. The simulation results show that the states of the proposed digital redesign technique closely match those of the conventional continuous-time PSS. The proposed digital redesign technique guarantees stability even with relatively slow sampling rates while Tustin’s method falls when sampling interval becomes larger.

델타 연산자를 이용한 관측기 기반 출력 궤환 퍼지 제어기의 디지털 재설계

본 논문은 미리 설계된 타카기-수게노 퍼지 모델 기반 아날로그 제어기를 상태 정합의 의미에서 등가인 샘플치 제어기로 효율적으로 변환하기 위해, 관측기 기반 출력 궤환 퍼지 제어기에 대한 지능형 디지털 재설계 기법을 제안한다. 아날로그 제어 시스템과 샘플치 제어 시스템 사이의 점근적 연관성을 위해 델타 연산자를 사용한다. 지능형 디지털 재설계 문제는 정합될 선형 연산자 간의 놈의 거리를 최소화하는 문제로 생각한다. 제어기 설계 조건은 선형행렬부등식의 형태로 유도되며, 디지털 재설계시 관측기와 제어기에 대한 분리 설계 조건이 만족함을 보인다. This paper addresses an intelligent digital redesign (IDR) technique for observer-based output-feedback control systems, in order to efficiently convert a pre-designed Takagi-Sugeno fuzzy model-based analog controller into a sampled-data one in the sense of state matching. A delta operator is used to get an asymptotic relation between the analog and the sampled-data control systems. The IDR problem is viewed as a minimization problem of the norm distances between linear operator to be matched. The condition is represented as linear matrix inequalities, and the separation principle on the IDR is shown.

Intelligent Digital Redesign for Nonlinear Interconnected Systems using Decentralized Fuzzy Control

In this paper, a novel intelligent digital redesign (IDR) technique is proposed for the nonlinear interconnected systems which can be represented by a Takagi-Sugeno (T-S) fuzzy model. The IDR technique is to convert a pre-designed analog controller into an equivalent digital one. To develop this method, the discretized models of the analog and digital closed-loop system with the decentralized controller are presented, respectively. Using these discretized models, the digital decentralized control gain is obtained to minimize the norm between the state variables of the analog and digital closed-loop systems and stabilize the digital closed-loop system. Its sufficient conditions are derived in terms of linear matrix inequalities (LMIs). Finally, a numerical example is provided to verify the effectiveness of the proposed technique. (13). Also, the robust IDR problem was studied for non- linear systems with parametric uncertainties (14). However, these papers dealt with the local state-matching without concerning the global one. The global approaches of the IDR problem were presented in (15-17), but they did not consider the interconnection of the nonlinear systems. The decentralized digital controllers for the interconnected systems were proposed in (18-20). But there were no studies about the IDR problem for the nonlinear inter- connected systems. In this paper, we propose a novel IDR method for the nonlinear interconnected systems which can be modelled by T-S fuzzy systems. The discretized models of the analog and digital closed-loop system with the decentralized con- troller are presented, respectively. Based on these discre- tized models, sufficient conditions are achieved for both the stability of the digital closed-loop system and the state- matching condition between analog and digital closed-loop systems. Its constructive conditions are presented in terms of linear matrix inequalities (LMIs). Finally, it shows the validity of the proposed ideas, techniques and procedures, through simple example. This paper is organized as follows: Section 2 describes the discretized models of the T-S fuzzy interconnected systems. The stability and state-matching conditions are proposed with the LMI form in Section 3. In Section 4, simulation example is provided to demonstrate the design procedures. Finally, the conclusions are given in Section 5.

Digital controller design for Bouc–Wen model with high-order hysteretic nonlinearities through approximated scalar sign function

In the models of piezoelectric actuator (PEA) systems, the hysteresis effects are often described by the concise Bouc–Wen models; however, these models are nonlinear and non-smooth because of the existence of terms which involve the absolute-value function. In particular, a challenging control problem is posed when, due to the properties of certain materials, such absolute-value terms are of high order. This control problem has been rarely studied. This article proposes the use of the approximated scalar sign function (ASSF), which is a numerically stable and differentiable nonlinear function, to represent the hysteresis function, with single-order or high-order absolute-value terms. This innovative step leads to a nonlinear but sufficiently smooth model. Then, a systematic digital design methodology is presented, which involves the following steps: (1) establish an optimal linear model based upon the resulting smooth model, (2) adopt a PI-based analogue controller and (3) apply the prediction-based digital redesign technique for digital implementation. A digital observer is also developed for state reconstruction, and to improve the input disturbance rejection. The positioning control of a PEA system with a high-order hysteretic Bouc–Wen model is implemented to demonstrate the effectiveness of the proposed ASSF based modelling and controller design approaches.

시변 추종제어기를 위한 디지털 재설계의 개선

Digital redesign is yet another efficient tool to convert a pre-designed analog controller into a sampled-data one to maintain the analog closed-loop performance in the sense of state matching. A rising difficulty in developing a digital redesign technique for trackers with time-varying references is the unavailability of a closed-form discrete-time model of a system, even if it is linear time-invariant. A way to resolve this is to approximate the time-varying reference as a piecewise constant one, which deteriorates the state matching performance. Another remedy may be to decrease a sampling period, which however could numerically destabilize the optimization-based digital redesign condition. In this paper, we develop a digital redesign condition for time-varying trackers by approximating the time-varying reference through a triangular hold and by introducing delta-operated discrete-time models. It is shown that the digitally redesigned sampled-data tracker recovers the performance of the pre-designed analog tracker under a fast sampling limit. Simulation results on the formation flying of satellites convincingly show the effectiveness of the development.

Iterative learning-based decentralized adaptive tracker for large-scale systems: A digital redesign approach

In this paper, a digital redesign methodology of the iterative learning-based decentralized adaptive tracker is proposed to improve the dynamic performance of sampled-data linear large-scale control systems consisting of N interconnected multi-input multi-output subsystems, so that the system output will follow any trajectory which may not be presented by the analytic reference model initially. To overcome the interference of each sub-system and simplify the controller design, the proposed model reference decentralized adaptive control scheme constructs a decoupled well-designed reference model first. Then, according to the well-designed model, this paper develops a digital decentralized adaptive tracker based on the optimal analog control and prediction-based digital redesign technique for the sampled-data large-scale coupling system. In order to enhance the tracking performance of the digital tracker at specified sampling instants, we apply the iterative learning control (ILC) to train the control input via continual learning. As a result, the proposed iterative learning-based decentralized adaptive tracker not only has robust closed-loop decoupled property but also possesses good tracking performance at both transient and steady state. Besides, evolutionary programming is applied to search for a good learning gain to speed up the learning process of ILC.

Optimal anti-windup digital redesign of multi-input multi-output control systems under input constraints

In this study, a novel optimal anti-windup control scheme is proposed to resolve the input constraint problem for multi-input multi-output (MIMO) systems, without losing the good tracking performance as possible. Avoiding complex numerical calculation, the proposed optimal control scheme can systematically compress a huge control input within the range of the required restriction by adjusting well-designed weighted matrices for linear constrained systems. Combining a conventional linear quadratic analogue tracker (LQAT) with the proposed scheme, the anti-windup-based optimal analogue tracker not only possesses the advantage of the conventional LQAT, good tracking performance, but also effectively resolves the input saturation problem. For practical consideration, the proposed LQAT is implemented by adopting the prediction-based digital redesign technique to design an effective digital control of linear MIMO sampled-data systems under input constraints.