Si-Lu Chen

Composite jerk feedforward and disturbance observer for robust tracking of flexible systems

Abstract In this paper, a novel feedforward controller for flexible motion systems is proposed based on both the rigid-body mode and lump-sum of the flexible modes. It only requires the reference trajectory to be defined up to its jerk, and gives well-behaved high-pass feedforward sensitivity. For systems with severe low-frequency disturbance, an additional disturbance observer is introduced, using the same jerk feedforward as the inversion of the nominal model. Remarkably, with such proposed control scheme and novel loop-shaping criteria, the improvement of disturbance rejection and profile tracking does not result in obvious degrading of the noise attenuation.

Integrated Mechatronic Design in the Flexure-Linked Dual-Drive Gantry by Constrained Linear–Quadratic Optimization

A dual-drive H-gantry is commonly used in many industrial processes to meet the requirement of high-precision Cartesian motion. Unlike the rigid-linked gantry stage, the flexure-linked counterpart allows a small degree of rotation of the crossarm to prevent possible damages. However, by this design, the chattering of control signals and inappropriate stiffness of the flexure may induce the resonant modes of the gantry. Hence, to maintain the precision tracking of the midpoint position and the orientation of the gantry, as well as to minimize the vibration on the end effector, we seek the most suitable flexure stiffness and controller parameters by formulating a constrained linear–quadratic optimization problem. Since such a mechatronic design problem is not solvable via standard linear–quadratic regulator formulas, we convert it to a constrained projection gradient-based optimization problem, which can be efficiently solved by direct computation of projection gradient and line search of optimal step length. A fast convergence of parameters is achieved after first several iterations. Through a series of comparative experiments, the effectiveness of the proposed method is validated.

A novel constrained H2 optimization algorithm for mechatronics design in flexure-linked biaxial gantry

The biaxial gantry is widely used in many industrial processes that require high precision Cartesian motion. The conventional rigid-link version suffers from breaking down of joints if any de-synchronization between the two carriages occurs. To prevent above potential risk, a flexure-linked biaxial gantry is designed to allow a small rotation angle of the cross-arm. Nevertheless, the chattering of control signals and inappropriate design of the flexure joint will possibly induce resonant modes of the end-effector. Thus, in this work, the design requirements in terms of tracking accuracy, biaxial synchronization, and resonant mode suppression are achieved by integrated optimization of the stiffness of flexures and PID controller parameters for a class of point-to-point reference trajectories with same dynamics but different steps. From here, an H2 optimization problem with defined constraints is formulated, and an efficient iterative solver is proposed by hybridizing direct computation of constrained projection gradient and line search of optimal step. Comparative experimental results obtained on the testbed are presented to verify the effectiveness of the proposed method.

Integrated mechatronics design of flexure joint and controller in dual-drive gantry: A constrained H 2 optimization approach

The dual-drive H gantry is widely used in many industrial processes that require high precision Cartesian motion. The conventional rigid-link version suffers breaking down of joints if any de-synchronization between the two carriages occurs. To prevent above potential risk, a novel biaxial gantry with flexure-links is designed to allow a small rotation angle of the cross-arm. Nevertheless, the chattering of control signals and inappropriate design of the flexure joint will possibly induce resonant modes of the end effector. Thus, in this work, the design requirements in terms of tracking accuracy, biaxial synchronization, and resonant mode suppression are achieved by integrated optimization of the stiffness of flexures and PID controller parameters for a class of point-to-point trajectories with same dynamics but different steps. From here, an H2 optimization with defined constraints is formulated, and an efficient iterative solver is proposed by hybridizing direct computation of constrained projection gradient and line search of optimal steps. Comparative experiments results obtained on the testbed are presented to verify the effectiveness of proposed method.

A novel robust, continuous, PID-assisted control for precision tracking of flexible systems a case study on timing belts

Low-cost, indirect-drive actuators, like timing belts are widely used in many industrial applications requiring linear translational motion. However, the timing belt faces greater control challenges as newer technological processes necessitate an increased tracking accuracy, precision and a need for minimal vibration all in the presence of rapid payload changes. Firstly, it is widely known that belt dynamics contribute higher order modes to the system. This causes a non-collocated control problem where the encoder position on the motor side does not provide a good estimate of the end-effector position. Second, these higher order modes coupled with Coulomb friction associated with the end-effector makes system identification tedious and inviable. In addition, this makes control tricky as standard discontinuous robust techniques have a tendency to excite those higher frequency dynamics. Furthermore, they are used to carry payloads of varying mass and are loaded and unloaded in quick succession adding to model uncertainty. In order to achieve higher position tracking accuracy, the authors propose a continuous robust controller that compensates for higher order disturbance while having a DOB that handles lower frequency, friction-related dynamics of the timing belt. In this paper, the details of this control scheme, simulation results justifying our approach and relevant stability proofs are presented.

Set-point alteration scheme for improved disturbance compensation

In precision motion control systems, the two degree of freedom (2-DOF) control structure is widely utilized for improving tracking performance. Although ideally the 2-DOF control can be designed to yield zero tracking error, the practical performance is often deteriorated due to disturbances. In some cases, the disturbances can be measured or estimated and then compensated by modifying the control input. However, in many industrial applications, the control engineers are not allowed to modify the control input directly, as the commercial controllers are often proprietary with a closed architecture. In order to address this practical difficulty, in this paper, we propose a disturbance compensation scheme which alters the set-point instead of the control input. Since we no longer have a preview of the altered set-point, the traditional feedforward controller is no longer implementable due to its non-causality. The non-causality problem is then solved by using a predictive feedforward approach, which is based on prediction of the set-point as well as a general offsetting mechanism to compensate for the prediction errors. Simulations are conducted to further illustrate the proposed method with a case study based on a timing-belt tracking setup.

Stiffness-oriented cable tension distribution algorithm for a 3-DOF Cable-driven variable-stiffness module

A modular cable-driven manipulator that consists of cable-driven joint modules can produce intrinsically-safe motions because of its light-weight structure and variable-stiffness property. In this paper, we focus on the issue of stiffness-oriented cable tension distribution for a 3-DOF 6-cable Cable-driven Spherical Joint Module (CSJM), which is modeled as a convex optimization problem. An algorithm based on Lagrange multiplier method and Karush-Kuhn-Tucker (KKT) Condition is employed to find the optimal cable tension solution. To validate the proposed algorithm, a simulation example with four cases is carried out. The result shows that the required stiffness can be successfully achieved through cable tension regulation.