Showing papers by "Richard H. Middleton published in 1998"
TL;DR: In this paper, exact, computable formulas for the frequency gain and L/sub 2/-induced norm of the sensitivity operator in a sampled-data control system with sampled data were developed.
Abstract: This paper develops exact, computable formulas for the frequency gain and L/sub 2/-induced norm of the sensitivity operator in a sampled-data control system. With sampled data, we refer to a system that combines both continuous-time and discrete time signals, which is studied in continuous time. The expressions are obtained using lifting techniques in the frequency domain and have application in performance and stability robustness analysis taking into account full intersample information.
16 citations
21 Jun 1998
TL;DR: In this article, the authors define concepts of plant and controller direction and alignment, and show that the closed-loop response depends upon the alignment between the plant and the controller, and that if alignment is poor, then using high gain will cause output sensitivity to be large and the closed loop system will exhibit large interactions.
Abstract: We describe properties of multivariable feedback control systems for which the plant has a single input and two outputs. Of particular interest are "algebraic" design trade-offs that occur between different feedback properties at the same frequency. We define concepts of plant and controller direction and alignment, and show that the closed loop response depends upon the alignment between plant and controller. In particular, if alignment is poor, then using high gain will cause output sensitivity to be large and the closed loop system will exhibit large interactions. We also discuss alignment in the case where gain is not necessarily large, and show that alignment is not important beyond the closed loop bandwidth. Also, the closed loop properties are not sensitive to modest amounts of misalignment. Finally, we show there exists a class of controllers that are always poorly aligned with the plant independently of the scaling used for the system outputs.
15 citations
16 Dec 1998
TL;DR: The cheap control tracking cost is shown to be a function of the plant non-minimum phase zeros and of the variation with frequency of the plants direction.
Abstract: A fundamental limitation exists in the achievable tracking performance of non-right-invertible systems. This limitation manifests itself in the cheap control tracking cost, which we show to be a function of the plant non-minimum phase zeros and of the variation with frequency of the plant direction. The cheap control tracking cost is further connected with an integral relation that constrains the performance of any stable closed-loop system where the plant has a single input and two outputs.
9 citations
16 Dec 1998
TL;DR: In this article, the authors investigate the robustness of sampled-data control systems to multiplicative uncertainty in the model of the continuous-time plant and argue that lightly damped controller poles, which may arise from attempting to cancel, or almost cancel, sampling zeros of the discretized plant are likely to introduce peaks into the fundamental complementary sensitivity function near the Nyquist frequency.
Abstract: In this paper, we investigate the implications for robust sampled-data feedback design of minimum phase sampling zeros appearing in the transfer function of discrete-time plants. Such zeros may be obtained by zero-order hold (ZOH) sampling of continuous-time models having relative degree two or greater. In particular, we address the robustness of sampled-data control systems to multiplicative uncertainty in the model of the continuous-time plant. We argue that lightly damped controller poles, which may arise from attempting to cancel, or almost cancel, sampling zeros of the discretized plant are likely to introduce peaks into the fundamental complementary sensitivity function near the Nyquist frequency. This in turn makes the satisfaction of necessary conditions for robust stability difficult for all but the most modest amounts of modeling uncertainty in the continuous-time plant. Some H/sub 2/- and H/sub /spl infin//-optimal discrete-time and sampled data designs may lead to (near-) cancellation, and we therefore argue that their suitability is restricted.
3 citations
16 Dec 1998
TL;DR: In this paper, the main contribution is a number of structure dependent stability results applicable to a class of hybrid systems modelled by discrete automata and formulated as two stability theorems giving necessary and sufficient conditions for global stability of synchronous and asynchronous piecewise linear hybrid systems.
Abstract: The main contribution of this paper is a number of structure dependent stability results applicable to a class of hybrid systems modelled by discrete automata. Our main results are formulated as two stability theorems giving necessary and sufficient conditions for global stability of synchronous and asynchronous piecewise linear hybrid systems. These theorems effectively reduce the hybrid systems stability analysis problem to analysis of stability of a certain class of linear time varying systems.
3 citations