Modern control engineering (3rd ed.)
Modern control engineering (3rd ed.)
Series of Abstractions for Hybrid Automata
HSCC '02 Proceedings of the 5th International Workshop on Hybrid Systems: Computation and Control
ICFEM '00 Proceedings of the 3rd IEEE International Conference on Formal Engineering Methods
A Hoare logic for single-input single-output continuous-time control systems
HSCC'03 Proceedings of the 6th international conference on Hybrid systems: computation and control
Formal verification of hybrid systems
EMSOFT '11 Proceedings of the ninth ACM international conference on Embedded software
A HOL theory of euclidean space
TPHOLs'05 Proceedings of the 18th international conference on Theorem Proving in Higher Order Logics
PVS linear algebra libraries for verification of control software algorithms in C/ACSL
NFM'12 Proceedings of the 4th international conference on NASA Formal Methods
Theorem Proving with the Real Numbers
Theorem Proving with the Real Numbers
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The accuracy of control systems analysis is of paramount importance as even minor design flaws can lead to disastrous consequences in this domain. This paper provides a higher-order-logic theorem proving based framework for the formal analysis of steady state errors in feedback control systems. In particular, we present the formalization of control system foundations, like transfer functions, summing junctions, feedback loops and pickoff points, and steady state error models for the step, ramp and parabola cases. These foundations can be built upon to formally specify a wide range of feedback control systems in higher-order logic and reason about their steady state errors within the sound core of a theorem prover. The proposed formalization is based on the complex number theory of the HOL-Light theorem prover. For illustration purposes, we present the steady state error analysis of a solar tracking control system.