Minimum energy control analysis of the switched reluctance stepper motor considering a nonlinear finite element model

Finite time linear quadratic based optimal control of BLDC motor employing distributed parameters modeling

“…Employing the linear quadratic control methodology and considering objective function (5) subject to (8), the control law is as follows [29]:…”

Infinite time horizon optimal current control of a stepper motor exploiting a finite element model

“…The motor is modelled using the time-stepping finite element technique. The formulation relies on a strong coupling between magnetic field, driving circuitry and mechanical motion equations yielding a complete description of the state of the motor at every time instance during the numerical iterative process [9,15,18,20]. In the field model the eddy current effect in the conducting regions of the rotor and stator cores is taken into account.…”

“…(1) and (2), i.e. unknown state space variables A and V , may be calculated by minimising the corresponding energy functional, the method well suited to systems with energy dissipation [15]. The above equations are well known but are shown here for completeness.…”

“…For minimisation of energy in the drive circuit, a linear quadratic performance index is a reasonable solution. It helps finding optimal waveforms of voltage excitation supplied to motor coils in terms of minimisation of energy delivered and power losses in windings resistance [9,11,15,18,19,21]. The assumed performance index for control in infinite time horizon takes the following form…”

“…This can be achieved by determining the optimal phase excitation switching angles, as discussed for example in [11] and [12]. Optimal energy control might also utilise shape and amplitude modulation of the excitation [13][14][15][16] or torque control enhancements by current waveform optimisation [1,17].…”