The Reaction Wheel Pendulum (RWP) is an interesting nonlinear system. A prototypical control problem for the RWP is to stabilize it around the upright position starting from the bottom, which is generally divided into at least 2 phases: (1) Swing-up phase: where the pendulum is swung up and moves toward the upright position. (2) Stabilization phase: here, the pendulum is controlled to be balanced around the upright position. Previous studies mainly focused on an energy method in swing-up phase and a linearization method in stabilization phase. However, several limitations exist. The energy method in swing-up mode usually takes a long time to approach the upright position. Moreover, its trajectory is not controlled which prevents further extensions. The linearization method in the stabilization phase, can only work for a very small range of angles around the equilibrium point, limiting its applicability. In this thesis, we took the 2nd order state space model and solved it for a constant torque input generating the family of phase-plane trajectories (see Appendix A). Therefore, we are able to plan the motion of the reaction wheel pendulum in the phase plane and a sliding mode controller may be implemented around these trajectories. The control strategy presented here is divided into three phases. (1) In the swing up phase a switching torque controller is designed to oscillate the pendulum until the system’s energy is enough to drive the system to the upright position. Our approach is more generic than previous approaches; (2) In the catching phase a sliding surface is designed in the phase plane based on the zero torque trajectories, and a 2nd order sliding mode controller is implemented to drive the pendulum moving along the sliding surface, which improves the robustness compared to the previous method in which the controller switches to stabilization mode when it reaches a pre-defined region. (3) In the stabilization phase a 2nd order sliding mode integral controller is used to solve the balancing problem, which has the potential to stabilize the pendulum in a larger angular region when compared to the previous linearization methods. At last we combine the 3 phases together in a combined strategy. Both simulation results and experimental results are shown. The control unit is National Instruments CompactRIO 9014 with NI 9505 module for module driving and NI 9411 module for encoding. The Reaction Wheel Pendulum is built by Quanser Consulting Inc. and placed in UT’s Advanced Mechatronics Lab. / text

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Thesis (Ph. D.)--University of Texas at Austin, 2006. / Vita. Includes bibliographical references.

Thesis (Ph. D.)--Ohio State University, 2007. / Title from first page of PDF file. Includes bibliographical references (p. 145-153).

This work describes the modeling, control design, and experimental verification of an electromagnetic suspension system with position feedback using infrared sensors. A nonlinear model is obtained by fitting a first principle analytical model of the system to experimental data. A sliding control strategy is designed using a sliding surface derived from the model to achieve robust stabilization for the closed-loop system. The control is then implemented on an embedded commercial DSP system for experimental verification of the designed control on a laboratory scale electromagnetic suspension system. To compensate for the steady-state tracking error, two modifications are considered. In the first method, a small magnitude integral term is added to the error feedback, equivalently adjusting the reference signal and eliminating the constant bias. In the second method, an integral sliding control is considered, using a higher-order sliding surface, which also eliminates the constant bias. The experimental results show the efficacy of all designed control techniques. The modified techniques, unlike the original design, effectively eliminate the constant position error.

abstract: Sliding-Mode Control (SMC) has several benefits over traditional Proportional-Integral-Differential (PID) control in terms of fast transient response, robustness to parameter and component variations, and low sensitivity to loop disturbances. An All-Digital Sliding-Mode (ADSM) controlled DC-DC converter, utilizing single-bit oversampled frequency domain digitizers is proposed. In the proposed approach, feedback and reference digitizing Analog-to-Digital Converters (ADC) are based on a single-bit, first order Sigma-Delta frequency to digital converter, running at 32MHz over-sampling rate. The ADSM regulator achieves 1% settling time in less than 5uSec for a load variation of 600mA. The sliding-mode controller utilizes a high-bandwidth hysteretic differentiator and an integrator to perform the sliding control law in digital domain. The proposed approach overcomes the steady state error (or DC offset), and limits the switching frequency range, which are the two common problems associated with sliding-mode controllers. The IC is designed and fabricated on a 0.35um CMOS process occupying an active area of 2.72mm-squared. Measured peak efficiency is 83%. / Dissertation/Thesis / Ph.D. Electrical Engineering 2013

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This thesis presents a torque control mechanism for switched reluctance machine (SRM) drives. The proposed mechanism is capable of maintaining ripple free torque control while minimizing the copper loss or mode-0 radial force or both at a fixed switching frequency. In the proposed approach, the torque control problem is addressed by splitting it into two parts. The first part consists of identification of optimum phase current references while the second part incorporates the design of an efficient current controller. For the identification of optimum phase current references, three algorithms are presented in the form of a developmental process. The nature of the online optimization problem is demonstrated using a simple 2-dimensional gradient descent method. Subsequently, a parametric form gradient descent algorithm is presented which transforms the original optimization problem into two 1-dimensional problems, viz. torque error minimization and identification of optimum search direction. This method yields improved computational efficiency and accuracy. The third algorithm incorporates projection using equality constraint on the phase torque contributions to achieve a 1-dimensional solution process. Although this algorithm takes more iteration as compared to the parametric form gradient descent algorithm, it demonstrates greater accuracy and computational efficiency. A comparative analysis of these algorithms is performed in at different operating conditions in terms of the torque ripple magnitude and computational effort. The thesis also presents a comprehensive analysis of well known control techniques for application in SRM current control in discrete-time domain. This analysis also presents a comparative evaluation of these control techniques under different operating conditions. On account of this analysis, several recommendations pertaining to the performance improvement are presented. Finally, a digital sliding-mode based model-free current controller suitable for fixed switching frequency operation is presented. The proposed controller is capable of providing a consistent dynamic response over wide operating range without utilizing any model information. The reference current tracking performance of this controller is verified through simulation studies in MATLAB/Simulink® environment and over a 1.2kW, 100V, 2500RPM, 12/8 experimental SRM drive. / Thesis / Doctor of Philosophy (PhD)

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