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2 Power Electronics and Drives

2 2023

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Nonlinear Optimal Control for the Nine-Phase Permanent Magnet Synchronous Motor

Rigatos Gerasimos.G., Siano Pierluigi, Al-Numay Mohammed, Abbaszadeh Masoud, Sari Bilal, Ouahada Khmaies

Power Electronics and Drives

2023

Vol. 8 (43)

380-402

Multi-phase electric motors and in particular nine-phase permanent magnet synchronous motors (9-phase PMSMs) find use in electric actuation, traction and propulsion systems. They exhibit advantages comparing to three-phase motors because of achieving high power and torque rates under moderate variations of voltage and currents in their phases, while also exhibiting fault tolerance. In this article a novel nonlinear optimal control method is developed for the dynamic model of nine-phase PMSMs. First it is proven that the dynamic model of these motors is differentially flat. Next, to apply the proposed nonlinear optimal control, the state-space model of the nine phase PMSM undergoes an approximate linearization process at each sampling instance. The linearisation procedure is based on first-order Taylor-series expansion and on the computation of the system’s Jacobian matrices. It takes place at each sampling interval around a temporary operating point which is defined by the present value of the system’s state vector and by the last sampled value of the control inputs vector. For the linearized model of the system an H-infinity feedback controller is designed. To compute the feedback gains of this controller an algebraic Riccati equation is repetitively solved at each time-step of the control algorithm. The global stability properties of the control scheme are proven through Lyapunov analysis. First it is demonstrated that the H-infinity tracking performance criterion is satisfied, which signifies robustness of the control scheme against model uncertainty and perturbations. Moreover, under mild assumptions it is also proven that the control loop is globally asymptotically stable. Additionally it is experimentally confirmed through simulation tests, that the nonlinear optimal control method achieves fast and accurate tracking of reference setpoints under moderate variations of the control inputs. Finally, to apply state estimation-based control without the need to measure the entire state vector of the nine-phase PMSM, the H-infinity Kalman Filter is used as a robust state estimator.

Nonlinear Optimal Control for a Gas Compressor Actuated by a Five-Phase Induction Motor

Rigatos Gerasimos.G., Abbaszadeh M., Sari B., Siano P.

Power Electronics and Drives

2023

Vol. 8 (43)

196-218

The article proposes a nonlinear optimal control method for the dynamic model of a gas centrifugal compressor being actuated by a five-phase induction motor (5-phase IM). To achieve high torque and high power in the functioning of gas compressors, 5-phase IM appear to be advantageous in comparison to three-phase synchronous or asynchronous electric machines. The dynamic model of the integrated compression system, which comprises the gas compressor and the 5-phase IM, is first written in a nonlinear and multivariable state-space form. It is proven that the electrically driven gas-compression system is differentially flat. Next, this system is approximately linearised around a temporary operating point that is recomputed at each sampling interval. The linearisation is based on first-order Taylor series expansion and uses the computation of the Jacobian matrices of the state-space model of the integrated system. For the linearised state-space description of the compressor and 5-phase IM, a stabilising optimal (H-infinity) feedback controller is designed. This controller achieves a solution to the nonlinear optimal control problem of the compressor and 5-phase IM system under model uncertainty and external perturbations. The feedback gains of the controller are computed by solving an algebraic Riccati equation at each iteration of the control method. Lyapunov analysis is used to demonstrate global stability for the control loop. Additionally, the H-infinity Kalman filter is used as a robust state estimator, which allows for implementing sensorless control for the gas compression system.