Methods of Ensuring Invariance with Respect to External Disturbances: Overview and New Advances

In this paper, we carry out a demonstration and comparative analysis of known methods of the synthesis of various control laws ensuring the invariance of the output (controlled) variable with respect to external disturbances under various assumptions about their type and channels of acting on the control plant. Methods of the synthesis are presented on the example of a third-order nonlinear system with single input and single output (SISO-systems), dynamic feedback synthesis is presented at a descriptive level and the focus is on procedures of static feedback synthesis. For the systems in which the matching conditions are not satisfied, it is concluded that it is expedient to introduce smooth and bounded nonlinear local feedbacks. Within the framework of the block control principle, we developed an iterative procedure of synthesis of S-shaped sigmoid feedbacks for such systems. Nonlinear local feedbacks ensure stabilization of the output variable with the given accuracy and settling time as in a system with traditionally used linear local feedbacks with high gains. However, in contrast to it, sigmoid functions do not lead to a large overshoot of state variables and control actions.

On perturbation range in the feedback synthesis problem for a chain of integrators system

The feedback synthesis problem for a chain of integrators system with continuous bounded unknown perturbation is considered. Our approach is based on the controllability function (CF) method proposed by V.I. Korobov. The perturbation range is determined by the negativity condition for the total derivative of the CF with respect to the perturbed system. The control that does not depend on perturbation under some restrictions and steers an arbitrary initial point from a neighborhood of the origin to the origin in a finite time (settling-time function) is constructed. The settling-time function depends on the perturbation, but it remains bounded from below and from above by the same value.

H2 gain-scheduled state-feedback synthesis conditions applied to a quadruple tank system

This article presents design conditions for controllers with polynomial dependence on the parameters for LPV systems.The technique is used to solve the problem of controlling a quadruple tank considering variations in valve opening. First, the nonlinear modeling of the system is presented as well with an analysis of its characteristics, and then an approximation to the dynamics is proposed in terms of a pure LPV polynomial model. As a main contribution, a sufficient condition based on LMIs is proposed for the design of scheduled controllers by state feedback with performance criterion based on the H2 norm. The design condition is general in the sense of treating LPV models with an arbitrary number of parameters and degree of polynomial dependence. Simulation in three distinct scenarios are presented to illustrate the design methodology and the quality of the controller designed for the quadruple tank.

Marine Autopilots’ Multipurpose Control Laws Synthesis for Actuators Time Delay

One analytical design problem involves constructing control laws for marine autopilot systems. Despite numerous known solutions, this problem can still be further developed by taking into account the actual conditions of the control system operation. An important issue for discussion is the feedback synthesis for marine ships with time delays in their rudders’ actuators. In this work, a new approach is proposed for providing all the desirable dynamic features of a closed-loop system with autopilot while taking into account the presence of a time delay. This approach is based on the predictive compensation of time delays via the specific transformation of an initially given reference controller with a special multipurpose structure. The applicability and effectiveness of the proposed method is further illustrated by a practical example of a controller design.