A Modified Stability Analysis of Two-Dimensional Linear Time Invariant Discrete Systems within the Unity-Shifted Unit Circle

This paper proposes a method to ascertain the stability of two dimensional linear time invariant discrete system within the shifted unit circle which is represented by the form of characteristic equation. Further an equivalent single dimensional characteristic equation is formed from the two dimensional characteristic equation then the stability formulation in the left half of Z-plane, where the roots of characteristic equation f(Z) = 0 should lie within the shifted unit circle. The coefficient of the unit shifted characteristic equation is suitably arranged in the form of matrix and the inner determinants are evaluated using proposed Jury’s concept. The proposed stability technique is simple and direct. It reduces the computational cost. An illustrative example shows the applicability of the proposed scheme.

Mixed sensitivity H_∞ control for LTI systems with varying time delays

Designing a robust controller for a system with timevarying delays poses a major challenge. In this paper, we propose a method based on mixed sensitivity H∞ for the control of linear time invariant（LTI） systems with varying time delays. The time delay is assumed bounded and the upper bound is known. In the technique we propose, the delay affecting the plant to be controlled is treated as an unmodeled uncertainty（in form of multiplicative uncertainty）. That uncertainty is approximated and then an H∞based controller, for the plant represented by the multiplicative uncertainty and the nominal model, is calculated. The obtained H∞controller is used to control the LTI systems with varying time delays. Simulation examples are given to illustrate the effectiveness of the proposed method.

Study on Four Disturbance Observers for FO-LTI Systems

This paper addresses the problem of designing disturbance observer for fractional order linear time invariant(FO-LTI) systems,where the disturbance includes time series expansion disturbance and sinusoidal disturbance.On one hand,the reduced order extended state observer(ROESO) and reduced order cascade extended state observer(ROCESO) are proposed for the case that the system state can be measured directly.On the other hand,the extended state observer(ESO) and the cascade extended state observer(CESO) are presented for another case when the system state cannot be measured directly.It is shown that combination of ROCESO and CESO can achieve a highly effective observation result.In addition,the way how to tune observer parameters to ensure the stability of the observers and reduce the observation error is presented in this paper.Finally,numerical simulations are given to illustrate the effectiveness of the proposed methods.

Design of high-speed and low-power finite-word-length PID controllers

ASIC or FPGA implementation of a finite word-length PID controller requires a double expertise： in control system and hardware design. In this paper, we only focus on the hardware side of the problem. We show how to design configurable fixed-point PIDs to satisfy applications requiring minimal power consumption, or high control-rate, or both together. As multiply operation is the engine of PID, we experienced three algorithms： Booth, modified Booth, and a new recursive multi-bit multiplication algorithm. This later enables the construction of finely grained PID structures with bit-level and unit-time precision. Such a feature permits to tailor the PID to the desired performance and power budget. All PIDs are implemented at register-transfer4evel （RTL） level as technology-independent reusable IP-cores. They are reconfigurable according to two compilemtime constants： set-point word-length and latency. To make PID design easily reproducible, all necessary implementation details are provided and discussed.