Two-degree-of-freedom compensator design for disturbance attenuation problem via higher order sinusoidal input describing functions theory

Abstract

In order to deal with disturbance attenuation problem in the presence of norm bounded uncertainties, different techniques involving [Formula: see text]/[Formula: see text] and linear quadratic regulator (LQR) designs exist in literature. The major drawbacks of these approaches may be classified as obtaining controllers with high order terms and too much computational load during the controller design. Hence, two-degree-of freedeom (2-DOF) controller design is taken into consideration in this study in order to avoid some of these drawbacks in the controller design and implementation process for disturbance attenuation problem. Here, the procedure for the design of 2-DOF structure is divided into two parts: designing [Formula: see text] controller to stabilize the closed loop system and implementing a higher order sinusoidal input describing functions (HOSIDF)-based compensator as a secondary controller in order to increase the disturbance attenuation performance of the overall closed loop system where the norm bounded uncertainties already exist. Thanks to the Lur’e type system definition that is also used in the design process of HOSIDF compensator, the research also proves that the proposed 2-DOF design structure is suitable to be implemented into the systems involving nonlinearities such as actuator saturation.

Bernstein polynomials based compensator design for coupled tank system with saturation nonlinearity

“…15 Some recent studies about HOSIDF theory also involve research papers dealing with nonlinear identification of a motion platform, 16 usage of HOSIDFs at the optimal sequence for reset controllers 17 and HOSIDF-based compensator design for disturbance attenuation problem. 18 The proposed frequency based compensator designed via HOSIDF theory in this study is structured in terms of Bernstein polynomials which are also used in different applications such as the development of mathematical algorithms for different purposes in literature. There exist studies that are carried out for the optimal stability of Bernstein basis.…”

“…15 Some recent studies about HOSIDF theory also involve research papers dealing with nonlinear identification of a motion platform, 16 usage of HOSIDFs at the optimal sequence for reset controllers 17 and HOSIDF-based compensator design for disturbance attenuation problem. 18…”

An ARX Model-Based Predictive Control of a Semi-Active Vehicle Suspension to Improve Passenger Comfort and Road-Holding

“…With the modelling issues addressed, the next step is to design the controller. The universe of control strategies reported for a 2-DOF one-quarter vehicle is diverse and includes a wide range of solutions, such as fuzzy controllers [19,20], H∞/H 2 solutions [21][22][23], sliding mode controllers [24,25], Linear Parameter-Varying control [26,27], Linear Quadratic regulator (LQR) [28], active suspension control with online estimation [29], among others. Moreover, complementary techniques to a pure control strategy have been developed to improve suspension performance in changing scenarios [30][31][32].…”