The Equilibrium Points and Stability of Grid-Connected Synchronverters

PI control of stable nonlinear plants using projected dynamical systems

“…We derive a sufficient condition on the controller gain that ensures closed-loop stability and reference tracking for a "naturally" feasible set of constant references. This result generalizes Lorenzetti and Weiss (2022), where a similar PI AW control strategy, using the saturating integrator introduced in Lorenzetti et al (2020), was formulated for SISO stable nonlinear plants. The PI SISO saturating integrator performs remarkably well in several applications, see, e.g., Lorenzetti and Weiss (2022); Lorenzetti et al (2022); Natarajan and Weiss (2017).…”

“…This result generalizes Lorenzetti and Weiss (2022), where a similar PI AW control strategy, using the saturating integrator introduced in Lorenzetti et al (2020), was formulated for SISO stable nonlinear plants. The PI SISO saturating integrator performs remarkably well in several applications, see, e.g., Lorenzetti and Weiss (2022); Lorenzetti et al (2022); Natarajan and Weiss (2017). We expect similar successful performance (and more) for its MIMO formulation shown in Fig.…”

“…In their work, the plant DC-gain sign assumption is replaced with an assumption on the monotonicity of the plant steady-state input-output mapping. The same approach has been used in our paper Lorenzetti and Weiss (2022) for the stability analysis of a stable nonlinear plant connected in feedback with a single-input singleoutput (SISO) low-gain anti-windup (AW) proportionalintegral (PI) controller. The recent paper Simpson-Porco (2020) on low-gain integral control for stable nonlinear systems, also employing SP tools, has generalized the main result from Desoer and Lin (1985).…”

“…Our aim is to formulate a simple novel AW MIMO lowgain PI controller for stable nonlinear systems, which forces the integrator state (and, thus, the steady-state plant input) to stay in a desired (compact and convex) region, using tools from projected dynamical systems (PDS) theory. We provide a rigorous closed-loop stability analysis, following the approach of Desoer and Lin (1985); Lorenzetti and Weiss (2022); Simpson-Porco (2020), by using SP theory results. We derive a sufficient condition on the controller gain that ensures closed-loop stability and reference tracking for a "naturally" feasible set of constant references.…”

“…In Sect. 3 the PI SISO saturating integrator from Lorenzetti and Weiss (2022) is reformulated as a MIMO controller, using tools from PDS theory, and the control problem is described in precise terms. Sect.…”