1,023 research outputs found
Dissipation-Induced Heteroclinic Orbits in Tippe Tops
This paper demonstrates that the conditions for the existence of a dissipation-induced heteroclinic orbit between the inverted and noninverted states of a tippe top are determined by a complex version of the equations for a simple harmonic oscillator: the modified Maxwell–Bloch equations. A standard linear analysis reveals that the modified Maxwell–Bloch equations describe the spectral instability of the noninverted state and Lyapunov stability of the inverted state. Standard nonlinear analysis based on the energy momentum method gives necessary and sufficient conditions for the existence of a dissipation-induced connecting orbit between these relative equilibria
Symbol-Based Control of a Ball-on-Plate Mechanical System
Modern control systems often consist of networks of components that must share a common communication channel. Not all components of the networked control system can communicate with one another simultaneously at any given time. The "attention" that each component receives is an important factor that affects the system's overall performance. An effective controller should ensure that sensors and actuators receive sufficient attention. This thesis describes a "ball-on-plate" dynamical system that includes a digital controller, which communicates with a pair of language-driven actuators, and an overhead camera. A control algorithm was developed to restrict the ball to a small region on the plate using a quantized set of language-based commands. The size of this containment region was analytically determined as a function of the communication constraints and other control system parameters. The effectiveness of the proposed control law was evaluated in experiments and mathematical simulations
On the Experiments about the Nonprehensile Reconfiguration of a Rolling Sphere on a Plate
A method to reconfigure in a nonprehensile way the pose (position and orientation) of a sphere rolling on a plate is proposed in this letter. The nonholonomic nature of the task is first solved at a planning level, where a geometric technique is employed to derive a Cartesian path to steer the sphere towards the arbitrarily desired pose. Then, an integral passivity-based control is designed to track the planned trajectory. The port-Hamiltonian formalism is employed to model the whole dynamics. Two approaches to move the plate are addressed in this paper, showing that only one of them allows the full controllability of the system. A humanoid-like robot is employed to bolster the proposed method experimentally
Dual PD Control Regulation with Nonlinear Compensation for a Ball and Plate System
The normal proportional derivative (PD) control is modified to a new dual form for the regulation of a ball and plate system. First, to analyze this controller, a novel complete nonlinear model of the ball and plate system is obtained. Second, an asymptotic stable dual PD control with a nonlinear compensation is developed. Finally, the experimental results of ball and plate system are provided to verify the effectiveness of the proposed methodology
Remote vibrometry recognition of nonlinear eigen-states for object coverage of randomly large size
For objects of “large” vibration size such as waves on the sea surface, the choice of measurement method can create different understandings of system behavior. In one case, laser vibrometry measurements of a vibrating bar in a controlled laboratory setting, variation in probe spot size can omit or uncover crucial structural vibration mode coupling data. In another case, a finite element simulation of laser vibrometry measures a nonlinearly clattering armor plate system of a ground vehicle. The simulation shows that sensing the system dynamics simultaneously over the entire structure reveals more vibration data than point measurements using a small diameter laser beam spot, regardless of the variation of footprint (coverage) boundaries. Furthermore, a simulation method described herein allows calculation of transition probabilities between modes (change-of-state). Wideband results of both cases demonstrate the 1/f trend explained within – that the energy of discrete structural vibration modes tends to decrease with increasing mode number (and frequency), and why. These results quantify the use of less expensive non-imaging classification systems for vehicle identification using the remote sensing of surface vibrations while mitigating spectral response distortion due to coverage variation on the order of the structural wavelength (spectral reduction or elimination)
Nonlinear model predictive low-level control
This dissertation focuses on the development, formalization, and systematic evaluation of a
novel nonlinear model predictive control (MPC) concept with derivative-free optimization.
Motivated by a real industrial application, namely the position control of a directional control
valve, this control concept enables straightforward implementation from scratch, robust
numerical optimization with a deterministic upper computation time bound, intuitive controller
design, and offers extensions to ensure recursive feasibility and asymptotic stability by
design. These beneficial controller properties result from combining adaptive input domain
discretization, extreme input move-blocking, and the integration with common stabilizing
terminal ingredients. The adaptive discretization of the input domain is translated into
time-varying finite control sets and ensures smooth and stabilizing closed-loop control. By
severely reducing the degrees of freedom in control to a single degree of freedom, the exhaustive
search algorithm qualifies as an ideal optimizer. Because of the exponentially increasing
combinatorial complexity, the novel control concept is suitable for systems with small input
dimensions, especially single-input systems, small- to mid-sized state dimensions, and simple
box-constraints. Mechatronic subsystems such as electromagnetic actuators represent this
special group of nonlinear systems and contribute significantly to the overall performance of
complex machinery.
A major part of this dissertation addresses the step-by-step implementation and realization
of the new control concept for numerical benchmark and real mechatronic systems. This dissertation
investigates and elaborates on the beneficial properties of the derivative-free MPC
approach and then narrows the scope of application. Since combinatorial optimization enables
the straightforward inclusion of a non-smooth exact penalty function, the new control
approach features a numerically robust real-time operation even when state constraint violations
occur. The real-time closed-loop control performance is evaluated using the example
of a directional control valve and a servomotor and shows promising results after manual
controller design.
Since the common theoretical closed-loop properties of MPC do not hold with input moveblocking,
this dissertation provides a new approach for general input move-blocked MPC
with arbitrary blocking patterns. The main idea is to integrate input move-blocking with
the framework of suboptimal MPC by defining the restrictive input parameterization as a
source of suboptimality. Finally, this dissertation extends the proposed derivative-free MPC
approach by stabilizing warm-starts according to the suboptimal MPC formulation. The
extended horizon scheme divides the receding horizon into two parts, where only the first
part of variable length is subject to extreme move-blocking. A stabilizing local controller
then completes the second part of the prediction. The approach involves a tailored and
straightforward combinatorial optimization algorithm that searches efficiently for suboptimal
horizon partitions while always reproducing the stabilizing warm-start control sequences in
the nominal setup
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