g-Lun Chen

Spatially Periodic Disturbance Rejection With Spatially Sampled Robust Repetitive Control

Repetitive controllers have been shown to be effective for tracking periodic reference commands or for rejecting periodic disturbances. Typical repetitive controllers are synthesized in temporal domain where the periods of the reference or disturbance signals are assumed to be known and stationary. For periodic references and disturbances with varying periods, researchers usually resort to adaptive and robust control approaches. For rotational motion systems where the disturbances or reference signals are spatially periodic (i.e., periodic with respect to angular displacement), the temporal period of the disturbance and reference signals will be inversely proportional to the rotational speed and vary accordingly. Motivating by reducing halftone banding for laser printers, we propose a design framework for synthesizing spatially sampled repetitive controller by reformulating a linear time-invariant system subject to spatially periodic disturbances using angular displacement as the independent variable. The resulting nonlinear system can be represented as a quasi-linear parameter-varying (quasi-LPV) system with the angular velocity as one of the varying state-dependent parameters. An LPV self-gain– scheduling controller that includes a spatially sampled repetitive control can be designed to take into consideration bounded model uncertainty and input nonlinearity, such as actuator saturation. Using the signal from an optical encoder pulse as a triggering interrupt, experimental results verified the effectiveness of the proposed approach in rejecting spatially periodic disturbances that cannot be compensated with fixed period temporal repetitive controllers. DOI: 10.1115/1.2837306

Efficient scheduling algorithms for robot inverse dynamics computation on a multiprocessor system

The problem of scheduling an inverse dynamics computation consisting of m computational modules to be executed on a multiprocessor system consisting of p identical homogeneous processors to achieve a minimum-scheduled length is presented. To achieve the minimum computation time, the Newton-Euler equations of motion are expressed in the homogeneous linear recurrence form, which results in achieving maximum parallelism. To speed up the searching for a solution, a heuristic search algorithm called dynamical highest level first/most immediate successors first (DHLF/MISF) is proposed to find a fast but suboptimal schedule. For an optimal schedule, the minimum-scheduled-length problem can be solved by a state-space search method. An objective function is defined in terms of the task execution time, and the optimization of the objective function is based on the minimax of the execution time. The proposed optimization algorithm solves the minimum-scheduled-length problem in pseudopolynomial time and can be used to solve various large-scale problems in a reasonable time.<<ETX>>

Formulating and solving a class of optimization problems for high-performance gray world automatic white balance

This paper provides new insights into methods performing automatic white balance for a digitally captured image. It is shown that automatic white balance may be formulated as an optimization problem with explicit definition of objective function, decision variables, and constraints. Three alternative methods of formulating the optimization problem are proposed. It is also shown that fuzzy inference rules, commonly utilized in existing literatures to evaluate to what degree an image satisfying the gray world assumption, may be incorporated into the objective function of the optimization problem. A two-stage adjustment law with constrained search direction is then proposed to update the decision variables. A gradient descent algorithm is employed to numerically solve the problem, which guarantees the convergence and that optimal white balance effort is achieved for most images. Experimental results and a comparative study justify that the proposed methods are preferable to existing methods with regard to the execution time, the algorithmic complexity, and the performance.

Compensating for spatially repetitive disturbance with linear parameter varying repetitive control

Repetitive controllers have been shown to work well for tracking periodic reference commands or for rejecting periodic disturbances in regulation applications. Typical repetitive controllers are synthesized in a temporal domain. For motor/gear transmission systems, disturbances due to gear eccentricity or tooth profile error are spatially periodic. This implies that the temporal frequency values for these two types of disturbances are proportional to the nominal angular velocity and vary accordingly. A repetitive controller designed based on the temporal information of disturbances cannot perform well as the spatially periodic disturbances also affect the nominal angular velocity. We reformulate the temporal domain system with respect to a spatial coordinate, which resulted in a nonlinear position invariant (NPI) system. By treating the angular velocity as varying but measurable parameters, the nonlinear NPI system can be treated as a linear parameter varying (LPV) system, for which an LPV gain-scheduling repetitive controller (LPVRC) with anti-windup can be designed. Experimental results on the velocity regulation of the photosensitive drum in a laser printer verified the effectiveness of the proposed LPVRC design.

Design and hardware implementation for a full-bridge phase-shift PWM DC/DC converter system with FPGA-based PI gain-scheduling control

This paper presents a high-performance design of dc-dc switching power converter system, which can deliver a regulated 0–50V and 0–15A output. The full-bridge phase-shift converter is realized with zero voltage switching and UCC3895 IC to achieve higher efficiency and pulse width modulation. For wide range of adjustable voltage output control, a PI gain-scheduling control scheme is proposed and implemented using a conventional FPGA chip. Experimental results justify the feasibility and performance of the proposed power converter control system.

Adaptive Repetitive Control for Uncertain Variable-Speed Rotational Motion Systems Subject to Spatially Periodic Disturbances

This paper extends the authors previous work on spatial-based repetitive control. We propose another repetitive control design for rotational motion systems required to operate at various speeds, and subject to structured parameter uncertainty and spatially periodic disturbances. To synthesize a repetitive controller in spatial domain, a linear time-invariant system is reformulated with respect to a spatial coordinate (e.g., angular displacement), which results in a nonlinear system. Adaptive feedback linearization is applied to linearize the system while seeking the correct system parameters online. Then, a spatial-based reduced-order repetitive controller along with a stabilizing controller is designed and operates in parallel with the adaptively feedback linearized system. The overall adaptive repetitive control system is thus robust to structured parameter uncertainty and spatially periodic disturbances under variable process speed. Feasibility and effectiveness of the proposed scheme is verified by simulation.

Robust spatially sampled controller design for banding reduction in electrophotographic process

An improved controller design and implementation technique for electrophotographic process (EP) was proposed. The new controller was modified from a previous design to address two additional issues for generic EP platforms, i.e., reducing position-dependent disturbances and reducing system sensitivity to manufacturing variations in EP engine and consumables. To handle position-dependent periodic disturbances, a digital repetitive controller was developed and implemented using spatial sampling. The result is a control algorithm that will take into account the variation of the nominal operating speed. Second, system variations due to manufacturing variations as well as consumable changes were incorporated into the design of a two degree of freedom (TDOF) robust controller. The controller is optimal in the sense that it minimizes the size of the sensitivity function from a set of disturbance signals to a set of measurable signals critical to print quality, e.g. photoconductor drum velocity or scan line spacing. A suitable trade-off between system performance and robustness to system modeling uncertainties was considered in the synthesis and optimization formulation. The effectiveness of the proposed controller design and implementation technique was numerically and experimentally verified. Printed samples demonstrated significant reduction in visible banding that was verified by reflectance measurement.

Spatially periodic disturbance rejection using spatial-based output feedback adaptive backstepping repetitive control

In this paper, we propose a new design of spatial-based repetitive control for rotational motion systems required to operate at varying speeds and subject to spatially periodic disturbances. The system has known model structure with uncertain parameters. To synthesize a repetitive controller in spatial domain, a linear time-invariant system is reformulated with respect to a spatial coordinate (e.g., angular displacement), which results in a nonlinear system. A nonlinear state observer is then established for the system. Adaptive backstepping is applied to the system with the state observer so as to stabilize the system and reduce the tacking error. Moreover, a spatial-based repetitive controller is added and operates in parallel with the adaptively backstepped system, which further reduces the tracking error. The overall output feedback adaptive backstepping repetitive control system is robust to structured parameter uncertainty, capable of rejecting spatially periodic disturbances under varying process speeds, and can be shown to be stable and produce bounded state estimated error and bounded tracking error under sensible assumptions. Finally, feasibility and effectiveness of the proposed scheme is verified by simulation.

Banding Artifact Reduction for a Class of Color Electrophotographic Printers With Underactuated Motor/Gear Configuration

A servo control architecture is proposed for a class of color electrophotographic printers with underactuated motor/gear configuration. The insufficiency and performance limitation of using single actuator (either motor or laser intensity control) to reduce periodic imaging artifact, i.e., banding, for this type of systems is presented. The proposed dual-actuator control scheme consists of a conventional Hinfin feedback controller and a nonlinear feedforward controller. The feedback controller regulates the motor velocity to reduce the effect of disturbances and system sensitivity on the intermediate transfer belt, and the feedforward controller modulates the laser intensity to compensate for the reflectance variation associated with the disturbances on the photoconductive drum. Experiments based on the proposed scheme are performed and show significant banding reduction on both the measured reflectance and the printed images.

Banding reduction in electrophotographic process

This paper proposes a new process control strategy for reducing banding artifacts in electrophotographic (EP) processes. EP banding artifact is shown to correlate to the fluctuation of the organic photoconductive (OPC) drum angular velocity. Improved regulation of the OPC drum rotational velocity under various process uncertainty and variations will significantly improve EP process stability and reduce the appearance of banding. The proposed control strategy includes two levels of OPC drum speed regulation. The first level, utilizes a loop shaping technique to incorporate a human visual system (HVS) model into the control loop to eliminate low frequency and non-periodic drum velocity fluctuation. The second level uses an internal model based repetitive controller to reduce the effect of periodic velocity fluctuations. The HVS based loop shaping design is intended to address the subjective evaluation of a printing process by incorporating human visual perception into EP process control. The experimental verification on a typical low cost 600-dpi EP engine showed significant banding reduction for spatial frequency up to 70 cycles per inch.