Inverted pendulum stabilization: Characterization of codimension-three triple zero bifurcation via multiple delayed proportional gains

The paper considers the problem of stabilization of systems possessing a multiple zero eigenvalue at the origin. The controller that we propose, uses multiple delayed measurements instead of derivative terms. Doing so, we increase the performances of the closed loop in presence of system uncertainties and/or noisy measurements. The problem formulation and the analysis is presented through a classical engineering problem which is the stabilization of an inverted pendulum on a cart moving horizontally. On one hand, we perform a nonlinear analysis of the center dynamics described by a three dimensional system of ordinary differential equations with a codimension-three triple zero bifurcation. On the other hand, we present the complementary stability analysis of the corresponding linear time invariant system with two delays describing the behavior around the equilibrium. The aim of this analysis is to characterize the possible local bifurcations. Finally, the proposed control scheme is numerically illustrated and discussed.     

An iterative method for suboptimal control of linear time-delayed systems

This article presents a new approach for solving the Optimal Control Problem (OCP) of linear time-delay systems with a quadratic cost functional. The proposed method can also be used for designing optimal control time-delay systems with disturbance. In this study, the Variational Iteration Method (VIM) is employed to convert the original Time-Delay Optimal Control Problem (TDOCP) into a sequence of nonhomogeneous linear two-point boundary value problems (TPBVPs). The optimal control law obtained consists of an accurate linear feedback term and a nonlinear compensation term which is the limit of an adjoint vector sequence. The feedback term is determined by solving Riccati matrix differential equation. By using the finite-step iteration of a nonlinear compensation sequence, we can obtain a suboptimal control law. Finally, Illustrative examples are included to demonstrate the validity and applicability of the technique.     

双输入双输出时延系统的系统预报控制

本文针对双输入双输出时延系统提出了脉冲响应系数预报控制和解耦控制，该方案具有较好的适应性。仿真结果证明了上述控制方案的有效性。     

On stability of second-order quasi-polynomials with a single delay

In this note the stability of a second-order quasi-polynomial with a single delay is studied. Although there is a vast literature on this problem, most available solutions are limited to some particular cases. Moreover, some published results on this subject appear to contain imprecise, or even wrong, conditions. The purpose of this note is to show that by accurate application of known theories, a complete explicit characterization of stability regions can be derived in a most general case. As a byproduct of the proposed analysis, we show that in the high-order case the quasi-polynomial is delay-independent unstable whenever its delay-free version has an odd number of unstable roots (or, equivalently, a negative static gain).     

Generalized multi-scale control scheme for cascade processes with time-delays

The cascade control is a well-known technique in process industry to improve regulatory control performance. The use of the conventional PI/PID controllers has often been found to be ineffective for cascade processes with long time-delays. Recent literature report has shown that the multi-scale control (MSC) scheme is capable of providing improved performance over the conventional PID controllers for processes characterized by long time-delays as well as slow RHP zeros. This paper presents an extension of this basic MSC scheme to cascade processes with long time-delays. This new cascade MSC scheme is applicable to self-regulating, integrating and unstable processes. Extensive numerical studies demonstrate the effectiveness of the cascade MSC scheme compared with some well-established cascade control strategies.     

带有检测迟延的燃料-汽压系统状态观测器设计

由于时延现象的大量存在,时延系统的状态估计问题得到了广泛的研究和重视.针对输出含有时间延迟的燃料-汽压系统,进行了时间延迟补偿观测器的设计.针对不同的时间延迟进行了仿真,实验结果表明,观测器在一定的时间内能够很好地跟踪输出时延系统的状态.     

Delay-dependent anti-windup synthesis for stability of constrained state delay systems using pole-constraints

This paper proposes the design of anti-windup compensator gain for stability of actuator input constrained state delay systems using constrained pole-position of the closed-loop. Based on Delay-Dependent Lyapunov-Krasovskii functionals and local sector conditions, a new LMI characterization is derived that ensures closed-loop asymptotic stability of constrained state delay systems while accounting upper bound fixed state delay and largest lower bound of the system’s pole-position in the formulation of anti-windup gain. Besides, at saturation, the method significantly nullifies the inherent slow dynamics present in the system. It is shown in the comparative numerical examples that the LMI formulation draws stability with improved time-domain performance.     

A predictive functional control algorithm for multivariable systems with time delay

To improve the dynamic characteristics and the coupling capability, a new predictive functional control algorithm is proposed for strong coupling multivariable systems with time delay, which combines predictive functional control and decoupliug control. First, a decoupling control algorithm is proposed, in which first-order models with time delay are established by analyzing the amplitude-frequency and phase-frequency characteristics of the decoupled subject. Then, a controller is designed for the single-variable subjects after decoupling based on the principles of predictive functional control. The simulation results show that this proposed algorithm has less online computation time and faster tracking. It can provide a more effective control for complex multivariable systems.     

A neural net-based time-delay compensation scheme and disturbance rejection for pneumatic systems

In practical electro-pneumatic or hydraulic servo mechanism, there is usually an unavoidable operating delay time in the solenoid valves. This may sometimes cause closed-loop instability if the time delay is not treated carefully in the control system designs. Furthermore, pneumatic actuators can offer high performance at low cost, but are often suffered from external disturbances depending on the operating conditions. This paper proposes a non-model-based design approach for pneumatic actuating systems. In the proposed control system, a gain scheduled fuzzy-PID controller ensures tracking performance an adaptable wavelet neuro compensator compensates for time-delay of the control valve, and a disturbance rejecter diminishes influence from load changes. A condition ensuring the closed-loop stability is derived. The proposed design is experimentally verified to show its effectiveness.     

线性时滞系统稳定性分析综述

时滞在工程领域广泛存在,对此综述了线性时滞系统的稳定性研究方法.从频域和时域两个角度详细介绍了各种方法的特点,着重讨论基于线性矩阵不等式(LMI)的分析方法,指出保守性是分析的重点.对现有结果的保守性进行比较和评述,并提出了改进的思路.