The balance of inverted pendulum on inclined surfaces is the precursor to their control in unstructured environments. Researchers have devised control algorithms with feedback from contact (encoders - placed at the pendulum joint) and non-contact (gyroscopes, tilt) sensors. We present feedback control of Inverted Pendulum Cart (IPC) on variable inclines using non-contact sensors and a modified error function. The system is in the state of equilibrium when it is not accelerating and not falling over (rotational equilibrium). This is achieved when the pendulum is aligned along the gravity vector. The control feedback is obtained from non-contact sensors comprising of a pair of accelerometers placed on the inverted pendulum and one on the cart. The proposed modified error function is composed of the dynamic (non-gravity) acceleration of the pendulum and the velocity of the cart. We prove that the system is in equilibrium when the modified error is zero. We present algorithm to calculate the dynamic acceleration and angle of the pendulum, and incline angle using accelerometer readings. Here, the cart velocity and acceleration are assumed to be proportional to the motor angular velocity and acceleration. Thereafter, we perform simulation using noisy sensors to illustrate the balance of IPC on surfaces with unknown inclination angles using PID feedback controller with saturated motor torque, including valley profile that resembles a downhill, flat and uphill combination. The successful control of the system using the proposed modified error function and accelerometer feedback argues for future design of controllers for unstructured and unknown environments using all-accelerometer feedback.
more »
« less
(2D+1) pendulum beams: non-diffracting optical spatial wavepackets that simulate quantum pendulum dynamics
The similarity between the 2D Helmholtz equation in elliptical coordinates and the Schr¨odinger equation for the simple mechanical pendulum inspires us to use light to mimic this quantum system. When optical beams are prepared in Mathieu modes, their intensity in the Fourier plane is proportional to the quantum mechanical probability for the pendulum. Previous works have produced a two-dimensional pendulum beam that oscillates as a function of time through the superpositions of Mathieu modes with phases proportional to pendulum energies.
Here we create a three-dimensional pendulum wavepacket made of a superposition of Helical Mathieu-Gaussian modes, prepared in such a way that the components of the wave-vectors along the propagation direction are
proportional to the pendulum energies. The resulting pattern oscillates or rotates as it propagates, in 3D, with
the propagation coordinate playing the role of time. We obtained several different propagating beam patterns
for the unbound-rotor and the bound-swinging pendulum cases. We measured the beam intensity as a function
of the propagation distance. The integrated beam intensity along elliptical angles plays the role of quantum
pendulum probabilities. Our measurements are in excellent agreement with numerical simulations.
more »
« less
- Award ID(s):
- 2011937
- NSF-PAR ID:
- 10337008
- Date Published:
- Journal Name:
- Complex Light and Optical Forces XVI, 1201704
- Volume:
- 1201704
- Page Range / eLocation ID:
- 51
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
We compare the electron dynamics at monocrystalline Cu(111), Au(100) and Pd(111) precursor substrates with vicinal nanosteps. The unoccupied bands of a surface superlattice are populated via the resonant charge transfer (RCT) between the surface and a H − ion that flies by at grazing angles. A quantum mechanical wave packet propagation approach is used to simulate the motion of the active electron, and time-evolved wave packet densities are used to visualize the dynamics through the superlattice. The survived ion fraction in the reflected beam generally exhibits modulations as a function of the vicinal terrace size and shows peaks at those energies that access the image state subband dispersions. Differences in magnitudes of the ion-survival as a function of the particular substrate selection and the ion-surface interaction time, based on the choice of two ion-trajectories, are examined. A square well model, producing standing waves between the steps on the surface, explains the energies of the maxima in the ion survival probability for all the metals considered. This indicates that the primary process of confinement induced subband formation is robust. The work may motivate measurements and applications of shallow-angle ion-scattering spectroscopy to access electronic substructures in periodically nanostructured surfaces.more » « less
-
more » « less
Abstract Learning by doing has proven to have numerous advantages over traditionally taught courses in which the instructor teaches the topic while students remain passive learners with little engagement. Although laboratories give hands-on opportunities for undergraduate mechanical engineering students, they have to wait for a semester for the lab course for instance the prerequisite of the vibrations and control laboratory is the mechanical vibrations course. Since the nature of the dynamics branch consisted of dynamics, vibrations, and control theory courses are highly mathematical, students struggle comprehending the introduced topic and relate the theory to its real-world application area. Furthermore, it’s almost impossible for an instructor to bring the existing educational laboratory equipment to the class since they are bulky and heavy. The advents in manufacturing technology such as additive manufacturing bring us more opportunities to build complex systems new materials.
This study presents the design, development, and implementation of low-cost, 3D printed vibratory mechanisms to be utilized in mechanical vibrations, control theory courses along with their associated laboratories. A pendulum, cantilever beam integrated with springs, and a rectilinear system consisted of two sliding carts, translational springs, and a scotch yoke mechanism are designed. The main parts of the mechanisms are 3D printed using polylactic acid (PLA), polyethylene terephthalate glycol (PETG), and thermoplastic polyurethane (TPU).
-
more » « less
Abstract Objective Solar ultraviolet (UV) radiation is ubiquitous in human life and well known to cause skin damage that can lead to harmful conditions such as erythema. Although sunscreen is a popular form of protection for some of these conditions, it is unclear whether sunscreen can maintain the mechanical barrier properties of skin. The objective of this study was to determine whether
in vitro thin‐film mechanical analysis techniques adapted for biological tissue are able to characterize the efficacy of commonly used UV inhibitors and commercial sunscreens to protect the biomechanical barrier properties of stratum corneum (SC) from UV exposure.Methods The biomechanical properties of SC samples were assayed through measurements of the SC's drying stress profile and delamination energy. The drying stresses within SC were characterized from the curvature of a borosilicate glass substrate onto which SC had been adhered. Delamination energies were characterized using a double‐cantilever beam (DCB) cohesion testing method. Successive DCB specimens were prepared from previously separated specimens by adhering new substrates onto each side of the already tested specimen to probe delamination energies deeper into the SC. These properties of the SC were measured before and after UV exposure, both with and without sunscreens applied, to determine the role of sunscreen in preserving the barrier function of SC.
Results The drying stress in SC starts increasing sooner and rises to a higher plateau stress value after UVA exposure as compared to non‐UV‐exposed control specimens. For specimens that had sunscreen applied, the UVA‐exposed and non‐UV‐exposed SC had similar drying stress profiles. Additionally, specimens exposed to UVB without protection from sunscreen exhibited significantly lower delamination energies than non‐UV‐exposed controls. With commercial sunscreen applied, the delamination energy for UV‐exposed and non‐UV‐exposed tissue was consistent, even up to large doses of UVB.
Conclusion In vitro thin‐film mechanical analysis techniques can readily characterize the effects of SC's exposure to UV radiation. The methods used in this study demonstrated commercial sunscreens were able to preserve the biomechanical properties of SC during UV exposure, thus indicating the barrier function of SC was also maintained. -
more » « less
Abstract The ignition of plasmas in liquids has applications from medical instrumentation to manipulation of liquid chemistry. Formation of plasmas directly in a liquid often requires prohibitively large voltages to initiate breakdown. Producing plasma streamers in bubbles submerged in a liquid with higher permittivity can significantly lower the voltage needed to initiate a discharge by reducing the electric field required to produce breakdown. The proximity of the bubble to the electrodes and the shape of the bubbles play critical roles in the manner in which the plasma is produced in, and propagates through, the bubble. In this paper, we discuss results from a three-dimensional direct numerical simulation (DNS) used to investigate the shapes of bubbles formed by injection of air into water. Comparisons are made to results from a companion experiment. A two-dimensional plasma hydrodynamics model was then used to capture the plasma streamer propagation in the bubble using a static bubble geometry generated by the DNS The simulations showed two different modes for streamer formation depending on the bubble shape. In an elliptical bubble, a short electron avalanche triggered a surface ionization wave (SIWs) resulting in plasma propagating along the surface of the bubble. In a circular bubble, an electron avalanche first traveled through the middle of the bubble before two SIWs began to propagate from the point closest to the grounded electrode where a volumetric streamer intersected the surface. In an elliptical bubble approaching a powered electrode in a pin-to-pin configuration, we experimentally observed streamer behavior that qualitatively corresponds with computational results. Optical emission captured over the lifetime of the streamer curve along the path of deformed bubbles, suggesting propagation of the streamer along the liquid/gas boundary interface. Plasma generation supported by the local field enhancement of the deformed bubble surface boundaries is a mechanism that is likely responsible for initiating streamer formation.
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1117/12.2627732
