Interconnection and damping assignment approach to control of PM synchronous motors

Robust Linear Control of (Chaotic) Permanent-Magnet Synchronous Motors With Uncertainties

“…Simplified -models are often used for instance, neglecting viscous friction-cf., [14], [10] or by considering the stator inductances to be equal, that is the case of the smooth-air-gap PM machines-cf. [15], [6], [13], [3], [5], [9].…”

“…As is often desirable in control theory and practice, the control goal is to be achieved for all initial conditions, i.e., one seeks for global results. Of particular interest (at least in electrical engineering and physics) is to drive the PMSM to a constant operating point from initial condi- tions leading to chaos in open loop cf., [8], [10], [14]. The latter two exploit the Hamiltonian structure of the PMSM, the design in [14] leads to a closed-loop system with multiple equilibria, and the result is shown to hold for almost all initial conditions.…”

“…Of particular interest (at least in electrical engineering and physics) is to drive the PMSM to a constant operating point from initial condi- tions leading to chaos in open loop cf., [8], [10], [14]. The latter two exploit the Hamiltonian structure of the PMSM, the design in [14] leads to a closed-loop system with multiple equilibria, and the result is shown to hold for almost all initial conditions. While no stability proof is provided in [8], the control is interesting in that it exploits the dissipative forces inherent in the system and yields good performance, in simulations.…”

“…In this paper, we revisit the problems of set-point (constant operating point) and tracking (time-varying operating regime) control of open-loop chaotic permanent-magnet synchronous machines (PMSM). This problem has attracted a number of researchers from different areas as witnessed by the variety of publications' fora: physics cf., [3], [4], (power) electronics cf., [5]- [7], electrical engineering (circuits) cf., [8]- [12]; besides the fact that the PMSM is a popular benchmark in the control community cf., [13], [14]. One of the key problems related to the PMSM is its natural chaotic behavior, for certain choices of parameters and initial conditions, see, e.g., [15], [16], [6], [11].…”

“…While no stability proof is provided in [8], the control is interesting in that it exploits the dissipative forces inherent in the system and yields good performance, in simulations. Adaptive set-point control algorithms are included in [14] (known parameters, unknown load) and in [4] (zero load, one unknown parameter, smooth-air-gap machine). Other papers aiming at annihilating chaos include [15] where the goal is to drive the machine to describe periodic orbits.…”