Unified CACSD Toolbox for Hybrid Simulation and Robust Controller Synthesis with Applications in DC-to-DC Power Converter Control

Abstract

The current article presents the design, implementation, validation, and use of a Computer-Aided Control System Design (CACSD) toolbox for nonlinear and hybrid system uncertainty modeling, simulation, and control using μ synthesis. Remarkable features include generalization of classical system interconnection operations to nonlinear and hybrid systems, automatic computation of equilibrium points for nonlinear systems, and optimization of least conservative uncertainty bounds, with direct applicability for μ synthesis. A unified approach is presented for the step-down (buck), step-up (boost), and single-ended primary-inductor (SEPIC) converters to showcase the use and flexibility of the toolbox. Robust controllers were computed by minimization of the H∞ norm of the augmented performance systems, encompassing a wide range of uncertainty types, and have been designed using the well-known mixed-sensitivity closed loop shaping μ synthesis method.

μ-Synthesis FO-PID for Twin Rotor Aerodynamic System

“…As future work, the proposed design method will be added into a next iteration of the toolbox initially proposed in [9] in order to automatically perform the fractional-order fixedstructure µ-synthesis. Also, the proposed method can be integrated into a control scheme with a decentralized controller having an extra nonlinear component which ensures that the robust stability and robust performance are also guaranteed for the nonlinear system.…”

“…As already known, the last optimization problem can be solved using the so-called D-K iteration [9,17]. This iterative procedure starts with a fixed D (usually considered the unitary system) and alternatively computes the controller K, by solving the H ∞ control problem with fixed D, and the D-scale factor, by solving the Parrot problem, as defined in [6], for each point from a frequency set Ω = {ω l = ω 1 < • • • < ω N = ω u } followed an approximation of the obtained solutions with a minimum phase system.…”

“…For the sensitivity function, the frequency performance indicators of the weighting function are the minimum bandwidth frequency ω B , which is inversely proportional with the rise time, the maximum magnitude A S at low frequencies, which imposes the maximum steady-state error, the peak magnitude M S , which limits the overshoot of the system, along with the imposed slope n S of the sensitivity function at low and medium frequencies [9]:…”

“…The solutions, initially proposed for H ∞ problem [7], and then for µ-synthesis [8] as well, are based on nonsmooth optimization techniques. A CACSD toolbox that manages to offer an end-to-end solution for designing a robust controller starting from a given plant is presented in [9].…”

Modeling and Control Simulation of Power Converters in Automotive Applications

“…Model development is often oriented toward fine-grained attention on certain aspects, such as voltage and current behavior, thermal patterns, or the subtleties of component magnetism. Still, this method restricts the scope for a thorough analysis of important scenarios, and 'destructive' testing is, thus, required to investigate difficult operational combinations [36][37][38][39]. By utilizing a multifaceted model that encompasses many components, these constraints are addressed.…”