Tesis y Trabajos de Investigación PUCP

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Energy-Based Control for the Cart-Pole System in Implicit Port-Hamiltonian Representation
(Pontificia Universidad Católica del Perú, 2020-03-19) Huamán Loayza, Alex Smith; Reger, Johann; Cieza Aguirre, Oscar B.; Pérez Zúñiga, Carlos Gustavo
This master thesis is devoted to the design, analysis, and experimental validation of an energy-based control strategy for the well-known benchmark cart-pole system in implicit Port-Hamiltonian (PH) representation. The control scheme performs two tasks: swingup and (local) stabilization. The swing-up controller is carried out on the basis of a generalized energy function and consists of bringing the pendulum trajectories from the lower (stable) position to a limit cycle (homoclinic orbit), which passes by the upright (unstable) position, as well as the cart trajectories to the desired point. The (local) stabilizing controller is designed under a novel algebraic Interconnection and Damping Assignment Passivity-Based Control (IDA-PBC) technique and ensures the upright (asymptotic) stabilization of the pendulum as well as the cart at a desired position. To illustrate the effectiveness of the proposed control scheme, this work presents simulations and real-time experiments considering physical damping, i.e., viscous friction. The results are additionally contrasted with another energy-based control strategy for the cart-pole system in explicit Euler-Lagrange (EL) representation.
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Tracking controller design for a nonlinear model of a gantry crane based on dynamic extension and robustification
(Pontificia Universidad Católica del Perú, 2015-11-19) Zárate Moya, José Luis; Reger, Johann; Elías Giordano, Dante Ángel
Overhead cranes are widely used in industry for transportation of heavy loads and are common industrial structures used in building construction, factories, and harbors, traditionally operated by experienced crane operators. The underlyng system consists of three main components: trolley, bridge, and gantry. Basically, the system is a trolley with pendulum. In normal operation, the natural sway of crane payloads is detrimental to the safe and efficient action. Other external disturbances parameters, wind for example, also affect the controller performance. Basically, a crane system is an underactuated system. This makes the design of its controllers complicated. Usually, this is done via the crane acceleration required for motion. The most important issues in crane motion are high positioning accuracy, short transportation time, small sway angle, and high safety. The main goal of this thesis is to achieve a robust controller design procedure, based on H∞ control theory, for a nonlinear model of a 3-D gantry crane system. The approach shall be compared with classic controllers in terms of attenuating the perturbation on the payload transportation. The model describes the position of the load, as well as the time derivatives of the position. In vew of this, flatness-based feedforward control has to be devised, accompanied by the design of an optimal linear and nonlinear feedback controller. The nomnal states can be used as optimization parameters and restrictions on stability, overshoot, position regulation, and oscillation angle, being independent of the load mass and depending on the rope length. The procedure is as follows. First, a dynamic nonlinear model of the system is obtained using the Lagrange equations of motion which describe the simultaneous travelling, crossing, lifting motions and the resultant load swing of the crane. Then, the system is exactly linearised by a dynamic extension. Next the closed-loop system, based on the linear quadratic regulator scheme, is probed and compared with the H∞ robust control system for compensating modeling errors and/or internal and external perturbation. Finally, simulation results are presented showing the efficiency of the proposed controller design scheme. Results are provided to illustrate the improved performance of the nonlinear controllers over classic pole placement and linear quadratic regulator approaches, testing its fast input tracking capability, precise payload positioning and minimal sway motion.

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