Verifying Band Convergence for Sampled Control Systems

Ezudheen, P and Afzal, ZR and Prabhakar, P and D'Souza, D and D'Souza, M (2020) Verifying Band Convergence for Sampled Control Systems. In: 12th International Symposium on NASA Formal Methods, NFM 2020, 11-15, May 2020, Moffett Field; United States, pp. 329-349.

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Abstract

We present a method to verify transient and settling time properties, called band convergence properties, of digitally controlled continuous systems, wherein we consider a linear dynamical system model for a plant and a PID controller. We consider the discrete-time sampled behavior of the closed loop system, and verify band convergence for the discrete-time behavior. The basic idea is to look for a box-shaped invariant for the system which is adequate to ensure that the system stays within the given band. We first give a technique to handle a general discrete-time system, but with determinate matrix entries. We then give a technique to handle discrete-time systems with matrices that lie in a range which over-approximate the matrix exponentials (which arise when we consider the discrete-time version of a continuous system), using the notion of an abstract discrete-time system. We have implemented the verification approach, and evaluate its efficacy on some popular Simulink models.

Item Type:	Conference Paper
Publication:	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Publisher:	Springer
Additional Information:	The copyright of this article belongs to Springer
Keywords:	Continuous time systems; Digital control systems; Discrete time control systems; Dynamical systems; Formal methods; Linear control systems; NASA; Three term control systems, Continuous system; Convergence properties; Digitally controlled; Discrete - time systems; Discrete time behavior; Discrete time version; Linear dynamical systems; Matrix exponentials, Closed loop systems
Department/Centre:	Division of Electrical Sciences > Computer Science & Automation
Date Deposited:	02 Sep 2020 09:09
Last Modified:	02 Sep 2020 09:09
URI:	http://eprints.iisc.ac.in/id/eprint/66438

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