Digital Redesign Research Articles

퍼지 펄스폭 변조 궤환 제어: 전역적 지능형 디지털 재설계 접근법

본 논문은 비선형 제어 시스템을 효과적으로 모사하는 TS(Takaki-Sugeno: TS) 퍼지 시스템의 펄스폭 변조 (Pulse-Width Modulated: PWM) 제환 제어기 설계 기법을 논의한다. 효율적이며 신뢰할만한 퍼지 PWM 제어기를 설계하기 위하여 전역적 지능형 디지털 재설계 기법(global intelligent digital redesign)을 이용한다. 우선 잘 설계된 아날로그 퍼지 제어기를 설계한 후 전역적 지능형 디지털 재설계 기법을 이용하여 디지털 퍼지 제어기를 설계한다. 유사한 전역적 상태정합 개념을 이용하여 재설계된 디지털 퍼지 제어기론 퍼지 PWM 제어기로 변환한다. 또한 재설계된 퍼지 PWM 제어기의 안정화 가능성을 조사한다. This paper discusses an intelligent digital redesign technique for designing a fuzzy pulse-width-modulated (PWM) control. First when we are given a well-designed fuzzy analog control, the equivalent digital control is intelligently redesigned. Using the similar technique we intelligently redesign the fuzzy PWM control from the intelligently redesigned fuzzy digital control. A stabilizability of the intelligently redesigned PWM control is rigorously analyzed.

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.

Optimal Dual-Rate Digital Redesign with Application to Missile Control

8Song, T. L., Shin, J. S., and Han, H. S., “Impact Angle Control for Planar Engagements,” IEEE Transactions on Aerospace and Electronic Systems, Vol. 35, No. 4, 1999, pp. 1439–1444. 9Song, T. L., and Shin, J. S., “Time Optimal Impact Angle Control for Vertical Plane Engagements,” IEEE Transactions on Aerospace and Electronic Systems, Vol. 35, No. 2, 1999, pp. 738–742. 10Savkin, A. V., Pathirana, P., and Faruqi, F. A., “The Problem of Precision Missile Guidance: LQR and H∞ Frameworks,” IEEE Transactions on Aerospace and Electronic Systems, Vol. 39, No. 3, 2003, pp. 901–910. 11Petersen, I. R., and Savkin, A. V., Robust Kalman Filtering for Signals and Systems with Large Uncertainties, Birkhauser, Boston, MA, 1999. 12Savkin, A. V., and Petersen, I. R., “Recursive State Estimation for Uncertain Systems with an Integral Quadratic Constraint,” IEEE Transactions on Automatic Control, Vol. 40, No. 6, 1995, pp. 1080–1083. 13Petersen, I. R., Ugrinovskii, V. A., and Savkin, A. V., Robust Control Design Using H∞ Methods, Springer-Verlag, London, 2000, Chap. 5. 14Savkin, A. V., and Petersen, I. R., “Nonlinear Versus Linear Control in the Absolute Stabilizability of Uncertain Linear Systems with Structured Uncertainty,” IEEE Transactions on Automatic Control, Vol. 40, No. 1, 1995, pp. 122–127. 15Singer, R. A., “Estimating Optimal Tracking Filter Performance for Manned Maneuvering Targets,” IEEE Transactions on Aerospace and Electronic Systems, Vol. 6, No. 4, 1970, pp. 473–483.

지능형 디지털 재설계를 이용한 비선형 인공위성의 디지털 PWM 정밀 자세 제어기의 개발

본 논문은 비선형 시스템을 위한 효율적인 펄스 폭 변조 (PWM: pulse-width-modulation) 제어기 설계 기법을 제안한다. 이를 위하여 우선 지능형 디지털 재설계 기법을 사용하여 잘 설계된 아날로그 제어기를 상태 정합(state-matching) 이라는 측면에서 그 제어 성능을 보장하도록 일반적인 펄스 크기 변조(PAM: pulse-amplitude-modulation) 디지털 제어기로 변환한다. 재설계된 지능형 PAM 디지털 제어기는 등가 영역의 원리(equivalent area principle)를 사용하여 PWM 제어기로 변환된다. 제안된 PWM 제어기법의 효용성을 검증하기 위하여 인공위성의 자세제어 시스템의 모의실험의 예를 보인다. This paper proposes a pulse-width-modulation (PWM) controller design technique using intelligent digital redesign. Intelligent digital redesign is to convert a well-designed analog fuzzy-model-based controller into an equivalent pulse-amplitude-modulation (PAM) digital controller maintaining the original analog control system in the sense of state-matching. In similar line of conversion concept, the redesigned PAM intelligent digital controller is converted into a PWM controller using the equivalent area principle. To convincingly visualize the proposed technique, an computer simulation example-attitude control of nonlinear artificial satellite system is included.

DISCRETIZED SUB‐OPTIMAL TRACKER FOR NONLINEAR CONTINUOUS TWO‐DIMENSIONAL SYSTEMS

ABSTRACTThe discretized quadratic sub‐optimal tracker for nonlinear continuous two‐dimensional (2‐D) systems is newly proposed in this paper. The proposed method provides a novel methodology for indirect digital redesign for nonlinear continuous 2‐D systems with a continuous performance index. This includes the following features: (1) the 2‐D optimal‐linearization approach of the nonlinear 2‐D Roesser's model (RM), (2) the dynamic programming‐based discretized quadratic optimal tracker for linear continuous 2‐D systems, (3) the steady‐state discretized quadratic sub‐optimal tracker for linear continuous 2‐D systems, and (4) the discretized quadratic sub‐optimal tracker for nonlinear continuous 2‐D systems. Illustrative examples are presented to demonstrate the effectiveness of the proposed procedure.

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.

Convergence of Sampled-Data Models in Digital Redesign

This note proposes sufficient conditions that guarantee uniform-in-time convergence, as the sampling period approaches zero, of the control input to and the controlled output of a plant under sampled-data control to those corresponding signals of the same plant under continuous-time control. Sampled-data control systems exhibiting such behavior are formally defined as sampled-data models, which can be very convenient in the analysis and design of sampled-data systems since they can warn the engineer if a known limiting closed-loop behavior is likely to be violated. This practical consideration often occurs in digital redesign, where an analog control law is implemented digitally, with the objective of preventing intersample ripples.

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.

A New Intelligent Digital Redesign for T–S Fuzzy Systems: Global Approach

This paper proposes a novel and efficient global intelligent digital redesign technique for a Takagi-Sugeno (T-S) fuzzy system. The term of intelligent digital redesign involves converting an existing analog fuzzy-model-based controller into an equivalent digital counterpart in the sense of state-matching. The proposed method should be notably discriminated from the previous works in that it allows us to globally match the states of the overall closed-loop T-S fuzzy system with the predesigned analog fuzzy-model-based controller and those with the digitally redesigned fuzzy-model-based controller, and further to examine the stabilizability by the redesigned controller in the sense of Lyapunov. The key idea is that the global intelligent digital redesign problem is viewed as a convex minimization problem of the norm distance between nonlinearly interpolated linear operators to be matched. Sufficient conditions for the global state-matching and the stability of the digitally controlled system are formulated in terms of linear matrix inequalities (LMIs). A complex nonlinear system, Duffing-like chaotic oscillator is simulated and demonstrated to validate the feasibility and effectiveness of the proposed digital redesign technique, which implies the safe applicability to the digital control system.

Combined H-Infinity Model-Matching Control and Dual-rate Digital Redesign for Missile Acceleration Autopilots

This paper proposes a missile acceleration autopilot obtained via H∞ model-matching control and dual-rate digital redesign. The first stage of the procedure consists in solving an H∞ model-matching problem in continuous-time. The second stage of the proposed approach is the conversion of the optimal continuous-time control system to a fast-inner-loop rate, slow-outer-loop rate digital control system using a dual-rate digital redesign approach which takes into account the closed-loop dynamics of the missile autopilot in the conversion. Reducing the order of the autopilot transfer functions and scheduling the controllers over the entire flight envelope constitute the last stages of the proposed approach. The proposed dual-rate missile acceleration autopilot is very useful in practice since it provides satisfactory closed-loop performances over an extended range of sampling rates, as compared with other digital autopilots. A nonlinear missile airframe dynamics model is used to demonstrate the application of ...

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.

An efficient observer-based sampled-data control: digital redesign approach

This brief concerns a new digital redesign (DR) technique for an observer-based output-feedback control (OBOFC) system. The term DR involves converting an analog controller into an equivalent digital one in the sense of state-matching. The considered DR problem is viewed as a convex minimization problem of the norm distances between linear operators to be matched and its constructive condition is formulated in terms of linear matrix inequalities (LMIs). The main features of the proposed method are that the state estimation error in the plant dynamics is considered for the state-matching condition that was ignored in the earlier works; the stability is guaranteed within the redesign procedure; the separation principle on the DR of the OBOFC is explicitly shown. A numerical example is included for visualizing the feasibility of the proposed technique.

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.

Discretized optimal tracker for continuous three-dimensional systems

The discretized quadratic optimal/sub‐optimal tracker and the continuous‐discrete Roesser model (RM) conversions for linear continuous three‐dimensional (3D) systems are newly proposed in this paper. The proposed optimal control approach provides a novel methodology for indirect digital redesign of a continuous 3D RM with a continuous cost function. Moreover, a sub‐optimal controller is newly presented, that decrease the overall memory size requirements of the optimal tracker. An Illustrative example is presented to demonstrate the effectiveness of the proposed methods.

Intelligent Digital Controller Using Digital Redesign

In this paper, a systematic design method of the intelligent PAM fuzzy controller for nonlinear systems using the efficient tools-Linear Matrix Inequality and the intelligent digital redesign is proposed. In order to digitally control the nonlinear systems, the TS fuzzy model is used for fuzzy modeling of the given nonlinear system. The convex representation technique also can be utilized for obtaining TS fuzzy models. First, the analog fuzzy-model-based controller is designed such that the closed-loop system is globally asymptotically stable in the sense of Lyapunov stability criterion. The simulation results strongly convince us that the proposed method has great potential in the application to the industry.

디지털 재설계를 이용한 관측기 기반 디지털 퍼지 제어기 설계

본 논문은 지능형 디지털 재설계 기법을 이용한 Takagi-Sugeno (T-S) 퍼지 시스템의 관측기 기반 출력 궤환 디지털 제어기 설계 기법을 제안한다. 지능형 디지털 재설계란 아날로그 퍼지 모델 기반 제어기를 등가의 성능을 발휘하는 퍼지 모델 기반 디지털 제어기로 변환하는 기법을 일컫는다. 여기서 등가의 성능은 상태 정합의 정확도를 의미한다. 본 연구에서 고려된 지능형 디지털 재설계 기법은 정합되어야 할 두개의 선형 작용소의 놈(norm)을 최소화하는 볼록 최적화 문제로 간주한다. 선형 행렬 부등식의 형태로 문제를 구성함으로써 재설계된 디지털 제어기에 의한 시스템의 안정가능성을 증명할 수 있다. 또한 제어기와 관측기의 재설계는 독립적으로 설계될 수 있음을 증명한다. This paper concerns a design methodology of observer-based output-feedback digital controller for Takagi-Sugeno(TS) fuzzy systems using intelligent digital redesign (IDR). The term of IDR involves converting an analog fuzzy-mode-based controller into an equivalent digital one in the sense of state-matching. The considered IDR problem is viewed as convex minimization problems of the norm distances between linear operators to be matched. The stability condition is easily embedded and the separations principle is explicitly shown.

디지털 재설계를 이용한 인공위성의 디지털 PWM 정밀 자세 제어기의 개발

본 논문은 디지털 재설계 기법을 이용한 펄스폭변조(PWM： pulse-width-modulation) 제어기 설계 기법을 제안한다. 디지털 재설계 기법은 잘 설계된 아날로그 제어기를 상태 정합(state-matching) 이라는 측면에서 그 제어 성능을 보장하도록 일반적인 펄스크기변조(PAM: pulse-amplitude-modulation) 디지털 제어기로 변환하는 기법이다 유사한 개념으로 재설계된 PAM 디지털 제어기는 등가 영역의 원리(equivalent area principle)를 사용하여 PWM 제어기로 변환된다. 제안된 PWM 제어기법의 효용성을 검증하기 위하여 인공위성의 자세제어 시스템의 모의실험의 예를 보인다. This paper concerns a pulse-width-modulation (PWM) controller design technique using digital redesign. Digital redesign is to convert a well-designed analog controller into an equivalent pulse-amplitude-modulation (PAM) controller maintaining the original analog control system in the sense of state-matching. In similar line of conversion concept, the redesigned PAM controller is converted into a PWM controller using the equivalent area principle. To convincingly visualize the proposed technique, an computer simulation example-attitude control of artificial satellite system is included.

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.

The observer‐based linear quadratic sub‐optimal digital tracker for analog systems with input and state delays

AbstractThis paper presents a new observer‐based sub‐optimal digital tracker for the continuous‐time system with input and state time delays. We directly convert the continuous‐time input‐state delayed system into an equivalent discrete‐time input‐state delayed model and its extended discrete‐time delay‐free model. In addition, we directly discretize the linear quadratic performance index specified in the continuous‐time domain into an equivalent decoupled discrete‐time performance index using the newly developed extended delay‐free model. As a consequence, the well‐developed discrete‐time optimal control theory for discrete‐time delay‐free system can be applied to determine the optimal digital tracker for the continuous‐time input‐state delayed system. When the states of the continuous‐time input‐state delayed system are not available for measurements, we develop a sub‐optimal digital observer for the original continuous‐time input‐state delayed system using the state‐matching digital redesign technique and the digital‐to‐analog model conversion technique. As a result, the proposed observer‐based linear quadratic digital tracker is able to make the output of the digitally controlled continuous‐time input‐state delayed system sub‐optimally track the desired reference signals. An illustrative example is presented to demonstrate the effectiveness of the proposed design methodology. Copyright © 2003 John Wiley & Sons, Ltd.