θ-D Approximation Technique for Nonlinear Optimal Speed Control Design of Surface-Mounted PMSM Drives

摘要

This paper proposes nonlinear optimal controllerand observer schemes based on a θ-D approximation approachfor surface-mounted permanent magnet synchronous motors(PMSMs). By applying the θ-D method in both the controllerand observer designs, the unsolvable Hamilton–Jacobi–Bellmanequations are switched to an algebraic Riccati equation and statedependentLyapunov equations (SDLEs). Then, through selectingthe suitable coefficient matrices, the SDLEs become algebraic, sothe complex matrix operation technique, i.e., the Kronecker productapplied in the previous papers to solve the SDLEs is eliminated.Moreover, the proposed technique not only solves the problem ofcontrolling the large initial states, but also avoids the excessiveonline computations. By utilizing a more accurate approximationmethod, the proposed control system achieves superior control performance(e.g., faster transient response, more robustness underthe parameter uncertainties and load torque variations) comparedto the state-dependent Riccati equation-based control method andconventional PI controlmethod. The proposed observer-based controlmethodology is tested with an experimental setup of a PMSMservo drive using a Texas Instruments TMS320F28335 DSP. Finally,the experimental results are shown for proving the effectivenessof the proposed control approach