The purpose of this paper is to introduce a new nonlinear optimal control method for the dynamic model of bearingless PMSMs. Compared to motors with active magnetic bearings, bearingless permanent magnet synchronous motors (BPMSM) are more compact, exhibit less failures and have a lower maintenance cost. They are very efficient in high-speed, high temperature and vacuum applications. They have found use in the starters/generators of aircrafts, in gas compressors, electrically assisted turbochargers, flywheel energy storage components and in centrifugal pumps. There are also several applications of theirs in the petroleum, natural gas and chemical industry. Therefore, the solution of the associated nonlinear control problem will have a positive impact in the deployment of the use of such motors.
Because of the coupling between the torque generating windings and their magnetic levitation windings, the functioning of bearingless motors is based on elaborated nonlinear and multivariable control methods. One can also distinguish different types of bearingless electric motors, such as induction, reluctance and permanent magnet synchronous ones. In this article a new nonlinear optimal (H-infinity) control method is developed for the dynamic model of the BPMSM.
It is proven that the dynamic model of the BPMSM is differentially flat, which comes to confirm the nonlinear controllability of this system. The dynamic model of the BPMSM undergoes approximate linearization through first-order Taylor series expansion around a temporary operating point Next, an H-infinity feedback controller is designed. To select the stabilizing feedback gains of the nonlinear optimal controller an algebraic Riccati equation is being solved repetitively, at each iteration of the control algorithm. The global stability properties of the control method are proven through Lyapunov analysis.
Because of the coupling between the torque generating windings and their magnetic levitation windings, the functioning of BPMSM is based on nonlinear and multivariable control methods. The new article proposes a nonlinear optimal control method for BPMSM which exhibits several advantages. The findings of the new article can be used in different types of bearingless electric motors, such as induction, reluctance and permanent magnet synchronous ones.
There are no practical constraints or implications. The dynamic model of the BPMSM undergoes approximate linearization with the use of first-order Taylor-series expansion around a time-varying operating point. For the approximately linearized model of the BPMSM an H-infinity optimal feedback controller is designed. To compute the controller’s stabilizing feedback gains an algebraic Riccati equation has to be solved repetitively at each time-step of the control algorithm. The global stability properties of the nonlinear optimal control scheme are proven through Lyapunov analysis.
The article’s nonlinear optimal control method for BPMSMs is expected to have a positive impact for several industrial applications and electromechanical systems which use these motors. BPMSMs have found use in the electric power industry and in the actuation of gas compressors and pumps. There are also several applications of theirs in the petroleum, natural gas and chemical industry. Obviously, the new article’s results on nonlinear optimal control of BPMSMs will create new products that will raise income and will bring significant earnings and economic benefits.
This study’s approach has extended the iterative Taylor-series based linearization concept to dynamical systems with a time-varying drift vector and time-varying control inputs gain matrix. Unlike Linear Parameter Varying (LPV) systems control, it does not need a transformation of the state-space model in the LPV form and does not need to solve a State-Dependent Riccati Equation (SDRE) either. Unlike Nonlinear Model Predictive Control (NMPC), it is of proven global stability and its convergence does not depend on initial conditions. Unlike Pontryagin’s optimal control it does not have to redefine a Hamiltonian function and does not need to compute iteratively the “adjoint coefficients”.
