ITAE optimal variable structure control of second order systems with input signal and velocity constraints

Abstract

Purpose -The purpose of this paper is to design a new sliding mode control algorithm for the second order dynamic system subject to input signal and velocity constraints. Design/methodology/approach -The proposed algorithm employs a time-varying switching line. At the initial time t ¼ t 0 , the line passes through the representative point of the system in the error state space. Afterwards, the line moves with a constant velocity and a constant angle of inclination to the origin of the space and having reached the origin it stops moving. Parameters of the line are selected in such a way that the integral of the time multiplied by the absolute error is minimized with the input signal and the system velocity constraints. First, each of the constraints is taken into account separately, and then both of them are considered at the same time. Findings -The algorithm introduced in this paper ensures insensitivity of the controlled system with respect to external disturbance and model uncertainty since the very beginning of its motion. Furthermore, the algorithm guarantees fast tracking error convergence to zero without overshoots or oscillations. Originality/value -In this paper, new systematic methods of the switching line design for the second order system are presented. Input signal and velocity constraints are explicitly taken into account in the design process.

Time-Varying Sliding Modes for Second and Third Order Systems

“…Some of the results have already been published in several journal (Bartoszewicz, 1995;Bartoszewicz, 1996;Bartoszewicz and Nowacka, 2004a;Bartoszewicz and Nowacka, 2005b;Bartoszewicz and Nowacka, 2005c;Bartoszewicz and Nowacka, 2006b;Bartoszewicz and Nowacka, 2006c;Bartoszewicz and Nowacka, 2006d;Bartoszewicz and Żuk, 2006;Bartoszewicz and Nowacka, 2007a;Bartoszewicz and Nowacka-Leverton, 2007) and conference papers (Bartoszewicz and Nowacka, 2004b;Bartoszewicz and Nowacka, 2005a;Nowacka and Bartoszewicz, 2005;Bartoszewicz and Nowacka, 2006a;Nowacka and Bartoszewicz, 2006a;Nowacka and Bartoszewicz, 2006b;Nowacka and Bartoszewicz, 2006c;Nowacka and Bartoszewicz, 2006d;Bartoszewicz and Nowacka, 2007b;Nowacka-Leverton and Bartoszewicz, 2008a;Nowacka-Leverton and Bartoszewicz, 2008b;Nowacka-Leverton and Bartoszewicz, 2008c), while various other derivations and conclusions presented in the two chapters have not been available in print yet. These two chapters comprise only original results obtained recently by the authors.…”

Optimized PID Controller Based on Beetle Antennae Search Algorithm for Electro-Hydraulic Position Servo Control System

“…The ITAE weights errors which exist after a long time and has an additional time multiplication in the error function, which emphasizes long duration errors and allows a faster response compared to the ISE and IAE. Thus, ITAE can solve problems more efficiently than other evaluation functions [43,44,45,46,47]. It has been shown that ITAE is a better evaluation function in the PID control system.…”