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An overhead crane with a flexible cable is an underactuated system; the vibration of the crane’s beam and the residual swinging of the payloads cause fatigue in the crane and affect the precise positioning of the payloads. In this paper, the coupling system of an overhead crane was simplified to that of a moving mass with pendulum swing passing beam model. The differential equation motion of a coupled overhead crane system was derived based on the Lagrange equation. Mathematical solution was carried out by using the Newmark-β integral method. The influences of the trolley’s acceleration and the parameters of the payloads on the vibration of the beam and the payloads’ swing were, respectively, analyzed. A numerical analysis of the results indicates that increasing the mass of the payloads leads to a larger deflection of the beam, whereas increasing the speed and acceleration of the trolley does not obviously influence the maximum deflection of the central beam.

An overhead crane is an underactuated system, which leads to residual swing of the crane’s payload when the crane accelerates or decelerates. This paper proposes a trajectory planning approach which uses the Bezier curve and particle swarm optimizer (PSO-BC) to limit the residual swing of a payload. The dynamic equation for an overhead crane is discredited, and a five-order Bezier curve is generated as the trolley’s displacement. The trolley’s desired position is set as the last control point of the Bezier curve, which guarantees that the trolley reaches the desired position accurately. Various constraints, including restricting the swing angle, the allowable trolley velocity, and the allowable trolley acceleration, are then taken into consideration as the constraints. In order to make the trolley reach its desired position whilst suppressing the payload’s swing under the constraints, a particle swarm optimizer is used to determine the optimal control point positions of the Bezier curve. Finally, the PSO-BC simulation results are compared to some existing approaches and are presented to show the feasibility and robustness of the proposed PSO-BC method. The simulation results indicate that the trolley moved to the desired position accurately whilst the payload’s swing angle is kept to an allowable level.

This paper presents an eight-channel time-interleaved (TI) 2.6 GS/s 8-bit successive approximation register (SAR) analog-to-digital converter (ADC) prototype in a 55-nm complementary metal-oxide-semiconductor (CMOS) process. The channel-selection-embedded bootstrap switch is adopted to perform sampling times synchronization using the full-speed master clock to suppress the time skew between channels. Based on the segmented pre-quantization and bypass switching scheme, double alternate comparators clocked asynchronously with background offset calibration are utilized in sub-channel SAR ADC to achieve high speed and low power. Measurement results show that the signal-to-noise-and-distortion ratio (SNDR) of the ADC is above 38.2 dB up to 500 MHz input frequency and above 31.8 dB across the entire first Nyquist zone. The differential non-linearity (DNL) and integral non-linearity (INL) are +0.93/−0.85 LSB and +0.71/−0.91 LSB, respectively. The ADC consumes 60 mW from a 1.2 V supply, occupies an area of 400 μm × 550 μm, and exhibits a figure-of-merit (FoM) of 348 fJ/conversion-step.