Meng-Shiun Tsai

Direct kinematic analysis of a 3-PRS parallel mechanism

Abstract This paper presents the direct kinematics solutions for a novel 3-PRS parallel mechanism. The geometric method is applied to formulate three coupled trigonometric equations. One algorithm for solving the three coupled equations is to use the Bezout’s elimination method which leads to a total of 64 solutions. By categorizing the 64 solutions into six groups and further examining the corresponding configuration for each group, the preferred solution to the direct kinematics problem can be obtained. The other approach for solving the coupled equations is to apply the optimization techniques with side and behavior constraints set by analyzing undesired configurations. This approach can obtain the preferred solution without checking all the possible solutions. Moreover, it can perform more efficiently than the elimination method.

Development of an integrated look-ahead dynamics-based NURBS interpolator for high precision machinery

Methodologies for planning motion trajectory of parametric interpolation such as non-uniform rational B-spline (NURBS) curves have been proposed in the past. However, most of the algorithms were developed based on the constraints of feedrate, acceleration/deceleration (acc/dec), jerk, and chord errors. The errors caused by servo dynamics were rarely included in the design process. This paper proposes an integrated look-ahead dynamics-based (ILD) algorithm which considers geometric and servo errors simultaneously. The ILD consists of three different modules: a sharp corner detection module, a jerk-limited module, and a dynamics module. The sharp corner detection module identifies sharp corners of a curve and then divides the curve into small segments. The jerk-limited module plans the feedrate profile of each segment according to the constraints of feedrate, acc/dec, jerk, and chord errors. To ensure that the contour errors are bounded within the specified value, the dynamics module further modifies the feedrate profile based on the derived contour error equation. Simulations and experiments are performed to validate the ILD algorithm. It is shown that the ILD approach improves tracking and contour accuracies significantly compared to adaptive-feedrate and curvature-feedrate algorithms.

Real-time NURBS interpolation using FPGA for high speed motion control

Modern motion control adopts NURBS (Non-Uniform Rational B-Spline) interpolation for the purpose of achieving high-speed and high-accuracy performance. However, in conventional control architectures, the computation of the basis functions of a NURBS curve is very time-consuming due to serial computing constraints. In this paper, a novel FPGA (Field Programmable Gate Array) based motion controller utilizing its high-speed parallel computing power is proposed to realize the Cox-de Boor algorithm for second and higher degrees NURBS interpolation. The motion control algorithm is also embedded in the FPGA chip to implement real-time control and NURBS interpolation simultaneously for multi-axis servo systems. The proposed FPGA-based motion controller is capable of performing the Cox-de Boor algorithm and the IIR (Infinite Impulse Response) control algorithm in about 46 clock cycles, as compared to the 1303 clock cycles by the traditional approach. Numerical simulations and experimental tests using an X-Y table verify the outstanding computation performance of the FPGA-based motion controller. The result indicates that shorter sampling time (10 @ms) can be achieved for NURBS interpolation which is highly critical to the success of high-speed and high-accuracy motion control.

Dynamic modeling and analysis of a bimodal ultrasonic motor

A dynamic model that includes four subsystems is developed to analyze the fundamental characteristics of a bimodal ultrasonic motor. The first subsystem is the driving circuit designed for the motor to achieve bidirectional motion. The stator is modeled as a Timoshenko beam, and the assumed mode energy method is used to obtain the dynamic equations. The normal interface force is represented by an elastic spring existing in between the tip of the stator and the moving platform. The interface forces are coupled into the dynamic formulations of the stator and the moving platform. The behavior of the force transmission between the stator and the moving platform are analyzed using the developed model. Transient and steady-state responses of the system are obtained by numerical simulation, and the results are validated by experiments. Furthermore, the existing of a nonlinear deadzone is predicted analytically, and the causes of this nonlinearity are clarified.

Development of command-based iterative learning control algorithm with consideration of friction, disturbance, and noise effects

In this brief, a command-based iterative learning control (ILC) architecture is proposed to compensate for friction effect and to reduce tracking error caused by servo lag. In contrast to a feedback-feedforward control structure, the proposed methodology utilizes the learning algorithm that updates the input commands based on the tracking errors from the previous machining process. The effects of noise accumulations from each learning process of the ILC are analyzed by formulating the equivalent error dynamic and updated command equations, and the P-type ILC with a zero-phase filter is applied to alleviate noise and disturbance effects. It is shown that, for tracking a circle, the quadrant protrusions caused by friction can be reduced substantially by the updated command containing a concave shape located at the crossing of the zero velocity. Finally, analytical simulation and experimental results demonstrate that the command-based ILC algorithm can enhance the tracking performance significantly.

Control of a ring structure with multiple active - passive hybrid piezoelectrical networks

A structural control concept, using multiple active - passive hybrid actuators (piezoelectric materials with active voltage sources and external passive RL circuits) on a ring structure, is investigated. A concurrent design method is developed to simultaneously optimize the active control gains and the values of the shunt resistors and inductors. A Kalman filter is employed to estimate the states of this multi-input - multi-output system from piezoelectric sensor measurements. Analysis results indicate that the proposed approach can suppress vibration and noise radiation effectively, and it can achieve better performance with less control effort as compared to a purely active system.

Integration of an Empirical Mode Decomposition Algorithm With Iterative Learning Control for High-Precision Machining

In this paper, a novel algorithm (ILC-EMD) that integrates iterative learning control (ILC) with empirical mode decomposition (EMD) is proposed to improve learning process. To explain the divergence behavior under the conventional ILC, the EMD is utilized to decompose the tracking error signal into 11 intrinsic mode functions (IMFs). By observing the root mean square and the correlation values of the IMFs during iterations, the first IMF is determined to be the undesired signal which could not be reduced by learning process. Furthermore, the command containing the first IMF could further excite the machine tool due to the resonance effects and cause the amplification of the error signal. The ILC-EMD can filter out the undesired signal and prevent the amplification effect. Experimental results on tracking the butterfly and dragon nonuniform rational B-spline curves validate the effectiveness of the ILC-EMD algorithm.

Dynamic Modeling and Decentralized Control of a 3 PRS Parallel Mechanism Based on Constrained Robotic Analysis

In this paper, a novel dynamic model is developed for analysis and control of a 3-PRS (Prismatic, Revolute, Spherical) parallel mechanism. The dynamic model is formulated in the joint space and three holonomic constraint equations are derived to specify the coupling relationships between the actuated legs and the moving platform. The associated constraint forces are determined to be internal forces and it leads to a novel model where the dynamics of the moving platform can be separated from that of the actuated legs. By utilizing the developed model, the constraint forces can be computed more efficiently as compared to the conventional approach. After compensation of the coupling dynamics, each actuated legs could be considered as a decoupled system. The coupling behavior of the parallel mechanism can then be easily illustrated by the proposed model. To facilitate real-time control implementation, the derived model can be further simplified and a decentralized control scheme integrated with a disturbance observer is proposed. The computational efficiency and tracking performances for the proposed control method are then validated by computer simulations.

Development of real-time look-ahead algorithm for NURBS interpolator with consideration of servo dynamics

In this paper, a real-time dynamics-based look-ahead (DBLA) algorithm for NURBS interpolator is proposed to generate a jerk-limited acceleration/deceleration (ACC/DEC) feedrate profile. The interpolator consists of three modules. The geometric module detects the local maximum/minimum (max/min) curvatures, and divides a NURBS curve into small segments. The dynamics module estimates contour errors at the sharp corners and adjusts the feedrates at the sharp corners. The jerk-limited module plans the feedrate profile of the curve according to the length of each segment and the given jerk limit. Simulations are performed to verify the real-time performance of the look-ahead algorithm. Finally, experiment results demonstrate that high-accuracy can be achieved with the proposed DBLA algorithm as compared to the adaptive-feedrate and the curvature-based feedrate interpolation algorithms.

A coupled robust control/optimization approach for active-passive hybrid piezoelectric networks

Active-passive hybrid piezoelectric networks (APPN) have been shown to be very effective in structural control. However, the issue of system robustness of such configurations has yet to be investigated. To ensure that the APPN concept still performs well under uncertainties, a coupled robust control (µ synthesis)/optimization approach is proposed to determine the active and passive parameters simultaneously with the consideration of system uncertainties. An analysis is performed to gain insight into both passive and active-passive hybrid systems. Through µ synthesis, it is also illustrated that the APPN approach can tolerate a much higher level of uncertainty than a purely active system.