Digital Redesign Method Research Articles

Decentralized observer-based tracker for analog systems with saturating actuator and state constraints

A weighted switching strategy and an inner-loop compensator are presented in this paper to design an observer-based tracker for a decentralized closed-loop cascaded system with a saturating actuator and state constraints. The LQR design methodology for the observer-based tracker is proposed to simplify the complexity of the decentralized control. The realizable sample-data controller with a low-gain property and a high design performance is realized through the digital redesign method. For obtaining a better design performance, evolutionary programming is then presented to tune the parameters of the tracker. Some examples are also presented to demonstrate the effectiveness of the proposed methodology.

완화된 안정도 조건을 갖는 강인한 디지털 퍼지 제어기 설계: 전역적 디지털 재설계 접근법

This paper presents the development of digital robust fuzzy controller for uncertain nonlinear systems. The proposed approach is based on the intelligent digital redesign(IDR) method with considering the relaxed stability condition of fuzzy control system. The term IDR in the concerned system is to convert an existing analog robust control into an equivalent digital counterpart in the sense of the state-matching. We shows that the IDR problem can be reduced to find the digital fuzzy gains minimizing the norm distance between the closed-loop states of the analog and digital robust control systems. Its constructive conditions are expressed as the linear matrix inequalities(LMIs) and thereby easily tractable by the convex optimization techniques. Based on the nonquadratic Lyapunov function, the robust stabilization conditions are given for the sampled-data fuzzy system, and hence less conservative. A numerical example, chaotic Lorentz system, is demonstrated to visualize the feasibility of the proposed methodology.

풍력과 태양 에너지를 이용한 하이브리드 발전시스템 구현을 위한 스위칭 디지털 퍼지 제어기 개발

본 논문에서는 하이브리드 발전 시스템에서의 최대 전력 추종을 위한 디지털 퍼지 제어기 설계를 목표로 한다. 하이브리드 발전 시스템은 풍력과 태양광, 두 개의 발전 시스템으로 구성된다. 각 발전기에서 전압과 전류는 일반적으로 비선형 관계에 있기 때문에, 퍼지 모델 기반 제어기를 사용하여 비선형성을 효율적으로 제어하게 된다. 또한 마이크로프로세서 기반제어 시스템의 구축을 위하여 최신 디지털 재설계 기법을 사용하며, 디지털 퍼지 제어기를 설계하게 된다. 마지막으로 하이브리드 발전 시스템의 플랜트를 통한 실험으로써 본 제안 기법의 우수성을 입증한다. We present the development of the digital fuzzy controller for maximum power regulation. A hybrid system that comprises wind and photovoltaic generation subsystems, and battery bank is developed in this paper. We use Takaki-Sugeno (T-S) fuzzy model to deal with the power regulation problem, since each power generator has complex nonlinear terms. The problem for regulation control can be simplified into a stabilization one. Also, in order to utilize the advanced digital device, we perform the intelligent digital redesign method. Finally, the performance of the proposed controller is extensively assessed through computer simulation.

Observer with evolutionary-programming-based optimal digital tracker for analog neutral multiple time-delay systems

In this paper, the finite-time optimal hybrid tracking control problem for analog neutral systems with multiple discrete and distributed time delays is formulated and studied. A novel approach that combining the evolutionary programming (EP) algorithm and the high-gain property for analog neutral multiple time-delay systems is proposed to achieve the “best” tracking performance for the first time. First, the Newton center interpolation formula and the linear interpolation formula, together with a modified rectangular rule and an augmented state vector, are utilized to construct the equivalent digital linear models. Next, according to the separation principle, the control gains of the digital tracker and the digital observer are designed separately by the discrete-time optimal control theory and prediction-based digital redesign method, and then combined together to form an observer-based optimal time-varying digital tracker. Eventually, the process is to combine the high-gain property with EP algorithm to search the optimal weighting matrices in the performance index to form an observer with EP-based low-gain digital tracker to achieve the objective of optimal tracking control. An example is given for illustrating the effectiveness of the new tracker design method.

불확실성을 갖는 비선형 시스템의 강인한 지능형 디지털 재설계

본 논문은 불확실성을 포함한 비선형 시스템에 대한 제어를 위해 강인 지능형 디지털 재설계의 전 역적 접근 방안에 대해 제안하고자 한다. 이산화를 통한 제어기 설계에 있어서 불확실성이 포함된 실시간 비선형 시스템에 대해 보다 효율적이고 안정적인 접근을 위해 T-S 퍼지 모델이 사용되었다. 그리고 전역적 접근을 위한 방안으로서 문제를 볼록 최적화 관점으로 변환 후, 오차가 가질 수 있는 놈의 영역을 최소화 하여 상태 접합을 이루고자 하였다. 또한 쌍선형과 역 쌍선형 기법을 사용함으로써 불확실성이 포함된 비선형 시스템을 보다. 더 정확하게 분석하였다. 샘플링 기간이 충분히 작다면, 불확실 비선형 시스템의 실시간 시스템으로의 전환이 충분한 이유를 가지게 된다. 전 역적 접근을 통한 디지털로 제어된 시스템은 선형 행렬 부등식 형태로 바꾸어 시스템의 안정성을 보장하고자 하였다. 마지막으로 T-S 퍼지 모델로 분석된 혼돈 Lorenz system에 적용함으로써 제안된 방법의 안정성과 효율성을 확인한다. This paper presents intelligent digital redesign method for hybrid state space fuzzy-model-based controllers. For effectiveness and stabilization of continuous-time uncertain nonlinear systems under discrete-time controller, Takagi-Sugeno(TS) fuzzy model is used to represent the complex system. And global approach design problems viewed as a convex optimization problem that we minimize the error of the norm bounds between nonlinearly interpolated linear operators to be matched. Also, by using the bilinear and inverse bilinear approximation method, we analyzed nonlinear system's uncertain parts more precisely. When a sampling period is sufficiently small, the conversion of a continuous-time structured uncertain nonlinear system to an equivalent discrete-time system have proper reason. Sufficiently conditions for the global state-matching of the digitally controlled system are formulated in terms of linear matrix inequalities (LMIs). Finally, a TS fuzzy model for the chaotic Lorentz system is used as an . example to guarantee the stability and effectiveness of the proposed method.

불확실성을 갖는 비선형 시스템을 위한 퍼지 모델 기반 제어기의 지능형 디지털 재설계

In this paper, we propose a systematic method for intelligent digital redesign of a fuzzy-model-based controller for continuous-time nonlinear system which may also contain system uncertainties. The continuous-time uncertain TS fuzzy model is first contructed to represent the uncertain nonlinear system. A parallel distributed compensation(PDC) technique is then used to design a fuzzy-model-based controller for both stabilization. The designed continuous-time controller is then converted to an equivalent discrete-time controller by using a globally intelligent digital redesign method. This new technique is designed by a global matching of state variables between analog control system and digital control system. This new design technique provides a systematic and effective framework for integration of the fuzzy-model-based control theory and the advanced digital redesign technique for nonlinear systems with uncertainties. Finally, Chaotic Lorenz system is used as an illustrative example to show the effectiveness and the feasibility of the developed design method.

Improved Digital Redesign for Fuzzy Systems: Compensated Bilinear Transform Approach

This paper presents a new intelligent digital redesign (IDR) method via the compensated bilinear transformation to design the digital controller such that the digital fuzzy system is equivalent to the analog fuzzy system in the sense of the state-matching. This paper especially consider a multirate control scheme with a predictive feature, where the digital control input is held constant N times between the sampling points. More precisely, the multirate control scheme is proposed that utilizes a numerical integration scheme to approximately predict the current state from the state measured at the sampling points, the delayed measurements. For this system, the IDR conditions incorporated with stabilizability in the format of the linear matrix inequalities (LMIs) are derived. The superiority of the proposed technique is convincingly visualized through a numerical example.

Powrer Series를 이용한 불확실성을 갖는 비선형 시스템의 지능형 디지털 재설계

This paper presents intelligent digital redesign method of global approach for hybrid state space fuzzy-model-based controllers. For effectiveness and stabilization of continuous-time uncertain nonlinear systems under discrete-time controller, Takagi-Sugeno(TS) fuzzy model is used to represent tile complex system. And global approach design problems viewed as a convex optimization problem that we minimize the error of the norm bounds between nonlinearly interpolated linear operators to be matched. Also, by using the power series, we analyzed nonlinear system`s uncertain parts more precisely. When a sampling period is sufficiently small, the conversion of a continuous-time structured uncertain nonlinear system to an equivalent discrete-time system have proper reason. Sufficiently conditions for the global state-matching of tile digitally controlled system are formulated in terms of linear matrix inequalities (LMIs). Finally, a TS fuzzy model for the chaotic Lorentz system is used as an example to guarantee the stability and effectiveness of the proposed method.

Evolutionary-programming-based tracker for hybrid chaotic interval systems

The nominal optimal tracker for the chaotic nonlinear interval system is first proposed in this thesis. First, we use an optimal linearization methodology to obtain the exact linear models of a class of discrete-time nonlinear time-invariant systems at operating states of interest, so that the conventional tracker can work for the nonlinear systems. A prediction-based digital tracker using the state-matching digital redesign method from a predesigned, state-feedback, continuous-time tracker for a hybrid chaotic system is presented. Then, we discuss the system has interval parameters. The interval system treated has interval and bounded parameters. The proposed evolutionary programming (EP) technique yields the strongest species to survive, reproduces themselves, and creates more outstanding offspring. The worst-case realization of the sampled-data nonlinear uncertain systems represented by the interval form with respect to the implemented best tracker is also found in this thesis for demonstrating the effectiveness of the proposed tracker. *The student **The advisor

Optimal dual-rate digital redesign with closed-loop order reduction

An optimal dual-rate digital redesign method is proposed that can be applied to continuous-time and fast-rate discrete-time control systems. The paper presents a technique, which relies on the solution of a dual-rate H2 discrete-time control problem, to convert such systems to either a slow-rate or a dual-rate sampled-data control system while guaranteeing closed-loop stability and performance in the discrete-time H2 sense. The proposed technique results in sampled-data control systems providing satisfactory closed-loop performances over an extended range of sampling rates, as compared with other widely used methods of digital redesign. Furthermore, the proposed digital redesign technique is useful in practice since it allows the designer to constrain the complexity of the digital controllers, thus resulting in low-order digital controllers easily implementable in software code and free of causality and real-time problems. Numerical examples provide a comparison of the proposed digital redesign technique with well-known approaches.

NEURAL NETWORK-BASED DIGITAL REDESIGN APPROACH FOR CONTROL OF UNKNOWN CONTINUOUS-TIME CHAOTIC SYSTEMS

This paper presents a neural network-based digital redesign approach for digital control of continuous-time chaotic systems with unknown structures and parameters. Important features of the method are that: (i) it generalizes the existing optimal linearization approach for the class of state-space models which are nonlinear in the state but linear in the input, to models which are nonlinear in both the state and the input; (ii) it develops a neural network-based universal optimal linear state-space model for unknown chaotic systems; (iii) it develops an anti-digital redesign approach for indirectly estimating an analog control law from a fast-rate digital control law without utilizing the analog models. The estimated analog control law is then converted to a slow-rate digital control law via the prediction-based digital redesign method; (iv) it develops a linear time-varying piecewise-constant low-gain tracker which can be implemented using microprocessors. Illustrative examples are presented to demonstrate the effectiveness of the proposed methodology.

불확실성을 갖는 단일 링크 유연로봇의 지능형 디지털 제어

In this paper, we propose a systematic method of a fuzzy-model-based controller for continuous-time nonlinear dynamical systems which may contain uncertainties. The continuous-time uncertain TS fuzzy model is first constructed to represent the uncertain nonlinear system. A parallel distributed compensation (PDC) technique is then used to design a fuzzy model based controller for both stabilization and tracking. Finally, the designed continuous-time controller is converted to an equivalent discrete-time controller by using an intelligent digital redesign method. This new design technique provides a systematic and effective framework for integration of the fuzzy model based control theory and the advanced digital redesign technique for nonlinear dynamical systems with uncertainties. Finally, the single link flexible-joint robot arm is used as an illustrative example to show the effectiveness and the feasibility of the developed design method.

Digital redesign of observer-based weighting switch controller for cascaded analog systems with state saturation and external loads

This paper presents an observer-based weighting switch controller for dealing with the problem of cascaded systems with state saturation and external loads. This method improves the generally poor transition response and output deviation caused by state saturation and external loads. In order to maintain the state-saturation limits, we adopt the evolutionary programming optimal search technique to find the optimal switching parameters for the weighted switch controller. Also, a digital redesign method is utilized to replace a designed high-gain analog controller with a low-gain digital controller. It is shown that the digitally redesigned outputs closely track the analogously controlled outputs. The digital redesign technique is then extended to find the digital version of the continuous-time observer. An illustrative example is demonstrated to show the effectiveness of the proposed procedure.

DIGITAL PID CONTROLLER DESIGN FOR DELAYED MULTIVARIABLE SYSTEMS

ABSTRACTA new methodology is proposed to design digital PID controllers for multivariable systems with time delays. Except for a few parameters that are preliminarily selected, most of the PID parameters are systematically tuned using the developed plant state‐feedback and controller state‐feedforward LQR approach, such that satisfactory performance with guaranteed closed‐loop stability is achieved. In order to deal with the modeling error owing to the delay time rational approximation, an IMC structure is utilized, such that robust stability is achieved, without need for an observer, and with improved online tuning convenience. Using the prediction‐based digital redesign method, the digital implementation is obtained based on the above‐proposed analog controller, such that the resulting mixed‐signal system performance will closely match that of the analog controlled system. An illustrative example is given for comparison with alternative techniques.

LIFTED DIGITAL REDESIGN OF PREDICTION-BASED DIGITAL CONTROLLER FOR HYBRID CHAOTIC SYSTEM

Tracking a periodic orbit of a chaotic attractor has been a considerable challenge since it often encounters numerical sensitivity. In this paper, a lifted prediction-based low-gain digital controller obtained from a predesigned high-gain analog controller is developed and applied to the hybrid chaotic system. The new proposed digital tracker with a relatively longer sampling time is insensitive to numerical errors and performs better than the one developed via the existing prediction-based digital redesign method. The Chen and Chua attractors are used as illustrative examples to demonstrate the effectiveness of the proposed lifted digital redesign method.

Lifted digital redesign of observer-based tracker for a sampled-data system

A lifted prediction-based digital redesign method to discretize an analogue tracker for a sampled-data systems is presented. The developed lifted digital redesign method is then used to construct a full/reduced-order digital observer. The developed lifted observer-based digital tracker improves the intersample behaviour of the digitally redesigned sampled-data systems. An illustrative example of a hybrid multivariable system demonstrates the effectiveness of the proposed method.

Digital redesign of analog Smith predictor for systems with input time delays

Abstract This paper presents a new methodology for digitally redesigning an existing analog Smith predictor control system, such that the cascaded analog controller with input delay can be implemented with a digital controller. A traditional analog Smith predictor system is reformulated into an augmented system, which is then digitally redesigned using the predicted intersampling states. The paper extends the prediction-based digital redesign method from a delay free feedback system to an input time-delay cascaded system. A tuning parameter v is optimally determined online such that in any sampling period, the output response error between the original analogously controlled time-delay system and the digitally controlled sampled-data time-delay system is significantly reduced. The proposed method gives very good performance in dealing with systems with delays in excess of several integer sampling periods and shows good robustness to sampling period selection.

불확실성을 갖는 동적 시스템에 대한 지능형 디지털 재설계

본 논문에서는 불확실성을 포함한 연속시간 비선형 동적 시스템에 대한 퍼지 모델 기반 제어기의 지능형 디지털 재설계를 위한 조직적인 방법을 제안한다. 불확실 비선형 시스템을 표현하기 위해 연속시간 불확실 TS 퍼지 모델이 구성되었다. 안정화와 추적을 위한 퍼지 모델 기반 제어기 설계를 위해 EPDC 기법이 이용되었다. 설계된 연속시간 제어기는 지능형 디지털 재설계 기법을 이용함으로써 이산시간 제어기로 전환되었다. 이 새로운 설계 기법은 퍼지 모델 기반 제어 이론과 불확실성을 가진 비선형 동적 시스템에 대한 진보된 디지털 재설계 기법의 통합을 위한 조직적이고, 효과적인 틀을 제공한다. 마지막으로, 단일 링크 유연 로봇 시스템의 모의 실험을 이용해 개발된 설계 방법의 효용성과 실행 가능성을 입증한다. In this paper, we propose a systematic method for intelligent digital redesign of a fuzzy-model-based controller for continuous-time nonlinear dynamical systems which may also contain uncertainties. The continuous-time uncertain TS fuzzy model is first constructed to represent the uncertain nonlinear systems. An extended parallel distributed compensation(EPDC) technique is then used to design a fuzzy-model-based controller for both stabilization and tracking. The designed continuous-time controller is then converted to an equivalent discrete-time controller by using an integrated intelligent digital redesign method. This new design technique provides a systematic and effective framework for integration of the fuzzy-model-based control theory and the advanced digital redesign technique for nonlinear dynamical systems with uncertainties. Finally, The single link flexible-joint robot arm is used as an illustrative example to show the effectiveness and the feasibility of the developed design method.

Reduced-order PIM methods for digital redesign

Complexity increase is common in modern global redesign methods and is tackled in this paper with a specific reference to the concept of plant input mapping. The paper proposes new global digital redesign techniques that rely on linear algebra to constrain the complexity of the resulting sampled-data control system while taking into account the plant dynamics and the topology of the continuous-time (CT) control system, and apply to any stable linear, time-invariant CT control system. Complexity is constrained in two ways. First, each discrete-time (DT) controller transfer function in the loop has an order which is fixed by the designer. Second, the number of DT controllers present in the loop is constrained by the designer. The proposed global digital redesign methods can be readily applied by the control designer as they require neither sophisticated mathematics nor stringent conditions for their application. The effectiveness of the proposed techniques is shown via numerical examples.

GA-based intelligent digital redesign of fuzzy-model-based controllers

Intelligent digital redesign involves converting a continuous-time fuzzy-model-based controller into an equivalent discrete-time counterpart for the digital control of continuous-time nonlinear systems by using the Takagi-Sugeno (TS) fuzzy models. In this paper, the authors present a new global state-matching intelligent digital redesign method for nonlinear systems by using genetic algorithms (GAs). More precisely, the intelligent digital redesign problem is converted to an equivalent optimization problem, and then GAs are adopted to find a solution. The search space, in which each problem variable is defined for GAs, are systematically obtained by the interval arithmetic operations. The proposed method results in global matching of the states of the analogously controlled system with those of the digitally controlled system while the conventional intelligent digital redesign method does not. The Chen's chaotic system is used as an illustrative example to show the effectiveness and the feasibility of the developed method. The proposed method provides a new approach for the digital redesign of a class of fuzzy-model-based controllers.