Leang-San Shieh

Effective chaotic orbit tracker: a prediction-based digital redesign approach

It has been widely experienced that tracking (targeting) a periodic orbit embedded within a chaotic attractor often encounters an essential issue of numerical sensitivity. In this paper, we develop an effective digital tracker for continuous-time chaotic orbit tracking, which is insensitive to numerical errors. The design is based on some advanced digital redesign techniques equipped with a predictive feature. The new digital tracker allows for a relatively large sampling time, which can be important in some applications such as in chaotic biological systems. A new chaotic attractor is used as an example for illustration and demonstration.

Hybrid state-space fuzzy model-based controller with dual-rate sampling for digital control of chaotic systems

We develop a hybrid state-space fuzzy model-based controller with dual-rate sampling for digital control of chaotic systems. A Takagi-Sugeno (TS) fuzzy model is used to model the chaotic dynamic system and the extended parallel-distributed compensation technique is proposed and formulated for designing the fuzzy model-based controller under stability conditions. The optimal regional-pole assignment technique is also adopted in the design of the local feedback controllers for the multiple TS linear state-space models. The proposed design procedure is as follows: an equivalent fast-rate discrete-time state-space model of the continuous-time system is first constructed by using fuzzy inference systems. To obtain the continuous-time optimal state-feedback gains, the constructed discrete-time fuzzy system is then converted into a continuous-time system. The developed optimal continuous-time control law is finally converted into an equivalent slow-rate digital control law using the proposed intelligent digital redesign method. The main contribution of the paper is the development of a systematic and effective framework for fuzzy model-based controller design with dual-rate sampling for digital control of complex such as chaotic systems. The effectiveness and the feasibility of the proposed controller design method is demonstrated through numerical simulations on the chaotic Chua circuit.

Load Disturbance Resistance Speed Controller Design for PMSM

This paper presents an linear-quadratic-regulator-based proportional-integral-differential equivalent controller design method for a permanent-magnet synchronous motor. The disturbance rejection is achieved based on a multi-objective observer in which observation error is purposely retained and utilized in load disturbance compensation. This makes disturbance rejection tuning independent of the adjustment for speed command tracking; and the disturbance compensation is an integrated part of the controller output, which reduces the chance of input or state saturation. A robust stability analysis is also included for the modeling error. The proposed methodology is implemented through the dSPACE digital signal processor system, and the experimental result confirms its effectiveness

Fuzzy Kalman filtering

The classical Kalman filtering (KF) algorithm has recently been extended to interval linear systems with interval parameters under the same statistical assumptions on noise, where the new algorithm is called Interval Kalman Filtering (IKF) scheme. The IKF algorithm has the same structure, and preserves the same optimality, as the classical KF scheme but provides interval-valued estimates. If the interval system has confidence description about the distribution of its interval values, we can further incorporate the IKF scheme with fuzzy logic inference, so as to develop a new filtering algorithm, called Fuzzy Kalman Filtering (FKF) algorithm. This algorithm preserves the same recursive mechanism of the KF and IKF, but produces a scalar-valued (rather than an interval-valued) estimate at each iteration of the filtering process. To compare the FKF to the IKF, computer simulation is included, which shows that the FKF is also robust against system parameter variations.

Linear quadratic regulators with Eigenvalue placement in a specified region

Two linear quadratic regulators are developed for placing the closed-loop poles of linear multivariable continuous-time systems within the common region of an open sector, bounded by lines inclined at +/- pi/2k (for a specified integer k not less than 1) from the negative real axis, and the left-hand side of a line parallel to the imaginary axis in the complex s-plane, and simultaneously minimizing a quadratic performance index. The design procedure mainly involves the solution of either Liapunov equations or Riccati equations. The general expression for finding the lower bound of a constant gain gamma is also developed.

On robust control of uncertain chaotic systems: a sliding-mode synthesis via chaotic optimization

Abstract This paper presents a novel Lyapunov-based control approach which utilizes a Lyapunov function of the nominal plant for robust tracking control of general multi-input uncertain nonlinear systems. The difficulty of constructing a control Lyapunov function is alleviated by means of predefining an optimal sliding mode. The conventional schemes for constructing sliding modes of nonlinear systems stipulate that the system of interest is canonical-transformable or feedback-linearizable. An innovative approach that exploits a chaotic optimizing algorithm is developed thereby obtaining the optimal sliding manifold for the control purpose. Simulations on the uncertain chaotic Chen’s system illustrate the effectiveness of the proposed approach.

Adaptive feedback linearization control of chaotic systems via recurrent high-order neural networks

In the realm of nonlinear control, feedback linearization via differential geometric techniques has been a concept of paramount importance. However, the applicability of this approach is quite limited, in the sense that a detailed knowledge of the system nonlinearities is required. In practice, most physical chaotic systems have inherent unknown nonlinearities, making real-time control of such chaotic systems still a very challenging area of research. In this paper, we propose using the recurrent high-order neural network for both identifying and controlling unknown chaotic systems, in which the feedback linearization technique is used in an adaptive manner. The global uniform boundedness of parameter estimation errors and the asymptotic stability of tracking errors are proved by the Lyapunov stability theory and the LaSalle-Yoshizawa theorem. In a systematic way, this method enables stabilization of chaotic motion to either a steady state or a desired trajectory. The effectiveness of the proposed adaptive control method is illustrated with computer simulations of a complex chaotic system.

Discretized quadratic optimal control for continuous-time two-dimensional systems

In this paper, discretized quadratic optimal control for continuous-time two-dimensional (2D) systems is newly proposed. It introduces a new state vector (a new virtual control input) to directly convert the original continuous-time 2D quadratic cost function into a decoupled discretized form. As a result, a new virtual discrete-time 2D model with the new virtual control input is constructed to indirectly find the desired discretized quadratic optimal regulator for the continuous-time 2D system. The recently developed dynamic programming in discrete-time 1D descriptor form is utilized to determine the desired discretized quadratic optimal regulator. This method provides a novel approach for discretized quadratic optimal control of continuous-time 2D systems. An illustrative example is presented to demonstrate the effectiveness of the proposed procedure.

Digital redesign of H8 controller via bilinear approximation method for state-delayed systems

Two issues are addressed: digitial modeling of the continuous-time state-delayed system; and digital redesign of the observer-based H8 controller for the continuous-time state-delayed system. The b...

Robust control of sampled-data uncertain systems using digitally redesigned observer-based controllers

This paper presents a new digital redesign method for robust control of a sampled-data uncertain system using an observer-based digital controller. The multiple-segment trapezoidal rule together with interval arithmetic is utilized to find a digital interval model of the original continuous-time uncertain system. A dual concept of the digital interval modelling, which captures the intersample states of the original continuous-time uncertain system is used to discretize a predesigned continuous-time state-feedback robust controller so that the states of the digitally controlled continuous-time uncertain system closely match those of the original analogously controlled continuous-time uncertain system. A discrete-time observer is constructed from the original continuous-time observer such that the estimated states of the redesigned discrete-time observer match those of the original continuous-time observer at the sampling instants. Using the newly digitally redesigned observer-based controllers, the resulting dynamic states of the digitally controlled sampled-data uncertain systems are able to match closely those of the original analogously controlled continuous-time uncertain systems.