Continuous-time Feedback Systems Research Articles

Sensitivity analysis of linear continuous-time feedback systems subject to control and measurement noise: An information-theoretic approach

Sensitivity of linear continuous-time SISO feedback systems, subject to control and measurement noise, is analyzed by deriving the lower bounds of Bode-like integrals via an information-theoretic approach. Bode integrals of four different sensitivity-like functions are employed to gauge the performance limitations of feedback systems. When the signals of the control system are stationary Gaussian, these four different Bode-like integrals can be represented as the differences between mutual information rates. These mutual information rates and hence the corresponding Bode-like integrals are proven to be bounded below by the unstable poles and zeros of the plant model, if the signals of the control system are wide-sense stationary.

A Simplified Approach to Analyze Complementary Sensitivity Tradeoffs in Continuous-Time and Discrete-Time Systems

A simplified approach is proposed to investigate the continuous-time and discrete-time complementary sensitivity Bode integrals (CSBIs) in this note. For continuous-time feedback systems with unbounded frequency domain, the CSBI weighted by $1/\omega^2$ is considered, where this simplified method reveals a more explicit relationship between the value of CSBI and the structure of the open-loop transfer function. With a minor modification of this method, the CSBI of discrete-time system is derived, and illustrative examples are provided. Compared with the existing results on CSBI, neither Cauchy integral theorem nor Poisson integral formula are used throughout the analysis, and the analytic constraint on the integrand is removed.

Indirect sampled-data control with sampling period adaptation

It is known that if a continuous-time feedback system is exponentially stable, then the corresponding sampled-data system obtained by sample-hold discretisation with constant sampling period is also exponentially stable, provided that the sampling period τ > 0 is sufficiently small. In general, it is difficult to estimate how small the sampling period has to be in order to achieve the stability of the sampled-data system. In this article, we present an adaptive mechanism for adjusting the sampling period. This mechanism has the properties that, for every initial state, (i) the adaptation of the sampling period terminates after finitely many time steps and (ii) the state of the adaptive sampled-data system is integrable and converges to zero as time goes to infinity.

Linear periodically time-varying scaling and its properties

Stimulated by a general necessary and sufficient condition for robust stability of sampled-data systems stated in an operator-theoretic framework, we introduce a novel technique called linear periodically time-varying (LPTV) scaling. We then give a simple example of sampled-data systems in which this new scaling allows exact robust stability analysis for static uncertainties while the conventional linear time-invariant (LTI) scaling fails to do so. This leads us to an interesting question whether LPTV scaling can be effective also in other situations, e.g., in the robust stability analysis of continuous-time feedback systems regarded as a special class of sampled-data systems, or for other classes of uncertainties. We thus study some basic properties of LPTV scaling by confining ourselves to the so-called D -scaling, and show that it provides no advantage over LTI scaling when it is applied to continuous-time LTI feedback systems, regardless of the class of uncertainties we take into consideration. This demonstrates that the LPTV scaling of the type we deal with in this paper is in some sense a special technique for sampled-data systems but is indeed an effective and more natural technique than the conventional LTI scaling as far as such systems are concerned. The technique can be further extended to include what is called noncausal LPTV scaling, and the implication of the present study in such a larger framework of LPTV scaling is also described.

Sufficient stability condition for a sampled-data system with digital controller

A quantitative stability condition for a sampled-data feedback system is formulated. The system is obtained from a stable continuous-time feedback system by digitalization of the controller. The condition shows how to determine a sampling frequency f/sub 0/ such that for all f larger than f/sub 0/ the discrete-time system remains stable.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Indirect robust totally decentralized adaptive control of continuous-time interconnected systems

This paper presents a global stability result on continuous-time indirect totally decentralized adaptive control systems. The algorithms employed in the design of local adaptive controllers are earlier basic conventional adaptive control algorithms subject to parameter projection operation. For the first time, it is shown that without any restriction on signals such as persistence of excitation, global boundedness of the signals in the overall continuous-time feedback system is guaranteed. For implementation, no a priori knowledge on the interactions and unmodeled dynamics is required.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>