Sound and Automated Synthesis of Digital Stabilizing Controllers for Continuous Plants

Abstract

Modern control is implemented with digital microcontrollers, embedded within a dynamical plant that represents physical components. We present a new algorithm based on counterexample guided inductive synthesis that automates the design of digital controllers that are correct by construction. The synthesis result is sound with respect to the complete range of approximations, including time discretization, quantization effects, and finite-precision arithmetic and its rounding errors. We have implemented our new algorithm in a tool called DSSynth, and are able to automatically generate stable controllers for a set of intricate plant models taken from the literature within minutes.

DSSynth: An automated digital controller synthesis tool for physical plants

“…Regarding the state-space representation, we have reproduced the stability property for the closed-loop control system of a pendulum represented by Eq. (7).…”

“…The DSSynth Toolbox can automatically synthesize stable and safe digital controllers for dynamic physical plants, represented in MATLAB either as a transfer function or a state-space equation. The DSSynth Toolbox is the first fully automated synthesis tool that is algorithmically and numerically sound, considering various error sources in the implementation of the digital control algorithm and in the computational modeling of plant dynamics [7], [8]. The DSSynth Toolbox presents a practical application of CEGIS-based program synthesis.…”

“…The proposed synthesis methodology for closed-loop digital control systems is based on the DSSynth tool [7], [8], which can be split into two main stages as follows: manual and automated steps, as illustrated in Fig. 4.…”

“…Our evaluation consists of 18 SISO control system benchmarks extracted from the literature [7], [8], [14], [15], [20]- [28], which include physical plants for an unmanned aerial Step Response Time (seconds) Amplitude Fig. 9:…”

“…We have recently proposed a new method to synthesize digital control systems for LTI systems, which we have named DSSynth (Digital-System Synthesizer) [7], [8]. The algorithm implements Counter-Example Guided Inductive Synthesis (CEGIS) [9].…”