Interconnection and damping assignment passivity-based control is a new controller design methodology developed for (asymptotic) stabilization of nonlinear systems that does not rely on, sometimes unnatural and technique-driven, linearization or decoupling procedures but instead endows the closed-loop system with a Hamiltonian structure with a desired energy function-that qualifies as Lyapunov function for the desired equilibrium. The assignable energy functions are characterized by a set of partial differential equations that must be solved to determine the control law. We prove in this paper that for a class of mechanical systems with underactuation degree one the partial differential equations can be explicitly solved. Furthermore, we introduce a suitable parametrization of assignable energy functions that provides the designer with a handle to address transient performance and robustness issues. Finally, we develop a speed estimator that allows the implementation of position-feedback controllers. The new result is applied to obtain an (almost) globally stabilizing scheme for the vertical takeoff and landing aircraft with strong input coupling, and a controller for the pendulum in a cart that can swing-up the pendulum from any position in the upper half plane and stop the cart at any desired location. In both cases we obtain very simple and intuitive position-feedback solutions.
The Permanent Magnet Synchronous Motors (PMSM) are extensively used in high-performance industrial applications. The electromagnetic torque in a PMSM is proportional to the angle between the stator and rotor flux linkages. Therefore, high dynamic response can be achieved by means of Direct Torque Control (DTC). However, because the rotor flux linkage is fixed on the rotor of PMSM, high torque ripple is produced when making use of full voltage vectors in classical DTC. The paper presents an improved PMSM DTC scheme by using a simplified space vector modulation technique, which addresses the problem by introducing a higher number of predefined voltage space vectors. The voltage vectors are tabulated in more precise switch tables which also take the emf induced in the stator windings into account. While still using switch tables to maintain the simplicity of the classical DTC scheme, the torque ripple results significantly decreased. Theoretical development and simulation results from the classical and improved DTC are presented and compared to support the research. Results show that the torque, flux linkage and stator current ripple are significantly decreased with the improved DTC.
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