Browsing by Subject "Nonlinear control"
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Item Gain Scheduled Control Using the Dual Youla Parameterization(2011-08-08) Chang, Young JoonStability is a critical issue in gain-scheduled control problems in that the closed loop system may not be stable during the transitions between operating conditions despite guarantees that the gain-scheduled controller stabilizes the plant model at fixed values of the scheduling variable. For Linear Parameter Varying (LPV) model representations, a controller interpolation method using Youla parameterization that guarantees stability despite fast transitions in scheduling variables is proposed. By interconnecting an LPV plant model with a Local Controller Network (LCN), the proposed Youla parameterization based controller interpolation method allows the interpolation of controllers of different size and structure, and guarantees stability at fixed points over the entire operating region. Moreover, quadratic stability despite fast scheduling is also guaranteed by construction of a common Lyapunov function, while the characteristics of individual controllers designed a priori at fixed operating condition are recovered at the design points. The efficacy of the proposed approach is verified with both an illustrative simulation case study on variation of a classical MIMO control problem and an experimental implementation on a multi-evaporator vapor compression cycle system. The dynamics of vapor compression systems are highly nonlinear, thus the gain-scheduled control is the potential to achieve the desired stability and performance of the system. The proposed controller interpolation/switching method guarantees the nonlinear stability of the closed loop system during the arbitrarily fast transition and achieves the desired performance to subsequently improve thermal efficiency of the vapor compression system.Item Nonlinear control with two complementary Lyapunov function(2016-12) Zelenak, Andrew J.; Landsberger, Sheldon; Pryor, Mitchell; Deshpande, Ashish; Fernandez, Benito; Kautz, DougIf a Lyapunov function is known, a dynamic system can be stabilized. However, computing or selecting a Lyapunov function is often challenging. This dissertation presents a new approach which eliminates this challenge: a simple control Lyapunov function [CLF] is assumed then the algorithm seeks to reduce the value of the Lyapunov function. If the control effort would have no effect at any iteration, the CLF is switched in an attempt to regain control. There is some flexibility in choosing these two complementary CLF’s but they must satisfy a few characteristics. The method is proven to asymptotically stabilize a wide range of nonlinear systems and was tested on an even broader variety in simulation. It was also tested on an industrial robot to provide compliant behavior. The simulated and hardware demonstrations provide a broad perspective on the algorithm’s usefulness and limitations. In comparison to the ubiquitous PID controller, the algorithm’s advantages include enhanced performance, ease of tuning, and extensions to higher-order and/or coupled systems. Those claimed advantages are validated by a test with four engineering students, which validates the controller as a viable option for nonlinear control (even at the undergraduate level). The algorithm’s drawbacks include the necessity of a dynamic model and, when linearization is required, the reliance on a small simulation time step; however, for the motivating application –interactive industrial robotic systems – both requirements were already met. Finally, the developed software was released to the public as part of the Robot Operating System (ROS) and the details of that release are included in this report.Item Sliding mode control of the reaction wheel pendulum(2014-12) Luo, Zhitong; Fernandez, Benito R.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.