Fixed Structure Feedforward Controller Design Exploiting Iterative Trials: Application to a Wafer Stage and a Desktop Printer

An underactuated multibody system has less control inputs than degrees of freedom. For trajectory tracking, often a feedforward control is necessary. Two different approaches for feedforward control design are presented. The first approach is based on a coordinate transformation into the nonlinear input–output normal-form. The second approach uses servo-constraints and results in a set of differential algebraic equations. A comparison shows that both feedforward control designs have a similar structure. The analysis of the mechanical design of underactuated multibody systems might show that they are nonminimum phase, i.e., they have unstable internal dynamics. Then the feedforward control cannot be computed by time integration and output trajectory tracking becomes a very challenging task. Therefore, based on the two presented feedforward control design approaches, it is shown that through the use of an optimization procedure underactuated multibody systems can be designed in such a way that they are minimum phase. Thus, feedforward control design using the two approaches is significantly simplified.

Feedforward control is widely applied on active vibration isolation system to attenuate vibration caused by base disturbance. Design of feedforward controller is conventionally based on plant model. Nevertheless, accurate plant model is normally not easy to be obtained. A data-driven feedforward control method is proposed in this paper to tackle this issue. In this method, no accurate plant model is needed and the problem of designing feedforward controller is formulated as a parameter optimization problem. By adopting FIR filter as feedforward controller structure, the parameter optimization problem is proved to be a convex optimization problem. A parameter iteration scheme based on Gauss-Newton algorithm is proposed to solve this parameter optimization problem. Gradient acquisition is achieved by Toeplitz matrix method. Employing certain step size, the optimal solution can be obtained with only one iteration. The proposed data-driven feedforward control method is validated by simulation and experiments. Experiments are conducted on a pneumatic spring active vibration isolation system.

This article presents a data-driven algorithm that combines the advantages of iterative feedforward tuning and disturbance rejection control to satisfy the precision requirements and ensure extrapolation capability of wafer scanning. The proposed algorithm differs from pre-existing algorithms in terms of its low requirement of system model, high extrapolation capability for non repetitive trajectory tracking tasks, and high tracking precision. The feedforward controller is tuned based on instrumental variables. It utilizes tracking errors from past iterations to eliminate reference-induced errors without requiring a system model. Meanwhile, the system inverse is approximated during iterative process, and then a disturbance rejection control based on iterative tuning is constructed to compensate for disturbance-induced errors. The proposed algorithm is applied to a wafer stage. The experimental results validate the effectiveness and superiority of the proposed algorithm.

This paper illustrates the synthesis of nonlinear feedforward controllers for chemical reactors. In most of the theoretical development and application of feedforward control only linear systems have been considered. There are, however, no inherent linear limitations in feedforward control. Since chemical reactors are usually nonlinear, the effectiveness of control should be improved by including nonlinearities in the design of feedforward controllers. This is particularly true for batch reactors because of the large changes in variables during a batch cycle. Continuous stirred‐tank reactors are studied with single and consecutive reactions of first and higher order. Effectiveness of linear and nonlinear feedforward controllers is compared for disturbances of various magnitude and direction. Feedforward control of batch and tubular reactors is also discussed.

A new method is proposed to design a feedforward controller for electromechanical servo systems. The settling time is minimized by iteratively solving a linear programming problem. A bound on the amplitude of the feedforward control signal can be imposed and the McMillan degree of the controller can be fixed a priori. We choose Laguerre basis functions for the feedforward filter. Since finding the optimal pole location is very difficult, we present a computationally cheap method to determine the pole location that works well in practice. Furthermore, we show how the method can account for plant and/or reference signal uncertainty. Uncertainty in servo systems can usually be modeled by additive norm-bounded dynamic uncertainty. We will show that, because the feedforward controller is designed for a finite-time interval, we can replace the dynamic uncertainty set by a parametric one. This allows us to design a robust feedforward controller by solving an LMI problem, under the assumption that the transfer functions of the plant, sensitivity, and process sensitivity depend affinely on the uncertainty. If the uncertainty set is a finite set, which is usually the case for uncertainty in the reference profiles, the feedforward design problem reduces to a linear program. These classes of uncertainty sets are well suited to describe variations in the plant and in the reference profile of a wafer stage, which is important for the practical application of the filter. Experimental results for a wafer stage demonstrate the performance improvement compared to a standard inertia feedforward filter.

Feedforward control can be considered as the most well-known control approach to deal with measurable disturbances. It started to be used almost 100 years ago, and since then it is being used in most industrial processes. It is a very simple technique that has been used typically as a complement to PID control, although it can be combined with any feedback controller. The feedforward control design has traditionally been performed assuming perfect cancellation of the disturbance signal, and when this solution was not possible because of non-realisable problems, static design solutions were usually implemented. In the last decade, this issue has been researched and analysed, and new designs for feedforward control have appeared to face these problems. As a result, a set of new simple tuning rules have been obtained providing considerable improvements in the control system performance. This paper presents a summary of these contributions and a short history of feedforward control.

On Optimal Feedforward and ILC: The Role of Feedback for Optimal Performance and Inferential Control

The design of a linear, reduced-order, continuous or discrete-time feedforward controller (FFC) is presented. The FFC is located in the reference value branch of a linear feedback system of any order which is designed according to the damping optimum. The aim of the FFC is to decrease the control system reference response time, while retaining a low overshoot and a well-damped form of the reference step response. This is achieved by locating the FFC zeros with the aid of the extended magnitude optimum, which is provided in the continuous or discrete-time variant. The influence of a suboptimally designed feedback system with a reduced-order feedback controller on feedforward control is analyzed. Reduced and full-order FFCs are compared.

<div class="section abstract"><div class="htmlview paragraph">The parameters determining shift quality control in automatic transmissions are determined as part of the calibration of the transmission control. The resulting control system typically has three components: feedforward control, where the control output is determined before a gearshift; feedback control, where the control output is determined during the gearshift based on sensed feedback; and learning control (adaptation), where the feedforward or feedback controller parameters are modified after the current gearshift has ended and before the next similar gearshift begins. Gearshifts involving the same ratio change are referred to here as similar gearshifts, though such gearshifts may involve differences in other variables such as vehicle speed or engine torque. In most automatic transmissions, gearshifts are controlled by hydraulic clutches, and operating conditions for these clutches may vary widely, requiring a dedicated transmission controller involving significant calibration effort.</div><div class="htmlview paragraph">In the current work, novel model-based methods are used to accomplish feedforward control of gearshifts, involving offline calibration of fill and torque phase control parameters and learning control of the fill phase. Towards this end, a physics-based model of the oncoming clutch involved in an upshift of a production automatic transmission was developed and experimentally validated against test bench experiments for a wide variety of inputs and operating conditions. The resulting model is used to generate a feedforward controller, offline model-based calibration algorithm, and a learning controller that corrects for clutch under-fill and over-fill. The effectiveness of the resulting controller is validated by simulation studies using the experimentally validated transmission hydraulic system model, in conjunction with a powertrain model. In particular, it is demonstrated that the learning controller corrects for initial under- or over-fill error in two to three gearshifts. Convergence and robustness properties, and transient performance of the learning controller are also discussed.</div></div>

ABSTRACTThe considered transport systems, which possess an actuator with a spatial influence characteristic along the transport path, are used for the transport of material between different process stages and for the conditioning of the conveyed goods at the same time. The spatially acting input results in complex input/output behaviour of a Single-Input Single-Output (SISO) system with distributed delays. The feedforward control task under consideration is defined by a setpoint change of the subsequent process stage. For the feedforward controller design, an inversion-based approach in the frequency domain is investigated to steer the output of the transport system towards a predefined constant value. In order to compensate model uncertainties and reject unknown disturbances, the results of the inversion-based feedforward control are used to design a feedback controller.

Hysteresis phenomena can significantly deteriorate the performance when performing servo tasks with piezoelectric actuators. The aim of this brief is to model this nonlinear hysteresis effect and use this model to develop a feedforward controller that compensates for the hysteretic behavior. Exploiting the dual-pair concept, a connection is established between hysteresis models and general memory (MEM) elements examplified by the Ramberg–Osgood model. This facilitates both a straightforward identification procedure of a hysteresis model and a feedforward controller design. Both the identification procedure and the feedforward controller are implemented on a piezoelectric actuator indicating a performance improvement by a factor 3.5.

Multivariable feedforward control design using disturbance cost maps and a genetic algorithm

This paper presents a new approach in the mitigation of unbalanced voltage sag by grid-connected voltage source converter (VSC). The feed forward (FF) controller architecture is adopted with the objective to minimize the impact of unbalanced voltage in the disruption of the dc-bus voltage. To deal with the existing independent control of active and reactive power, two FF controllers are needed. The first FF controller trims the dc-voltage controller output signal and provides correction for the d-axis current (active power) reference. The other feed forward controller trims the reactive/voltage support controller output signal to provide correction on the q-axis current (reactive power) reference. The computation elements of the FF controller are based on the linearized grid model in synchronous frame. The FF controller is tuned at -2ω1 which is the frequency in synchronous frame where the unbalanced voltage takes place. For verification of the proposed controller feasibility, simulation is used. The results show that the proposed FF controllers can seek to minimize the impact of unbalanced voltage sag particularly in maintaining the oscillating voltage closer to the dc-voltage reference point.

Contact force control of a propeller-driven system has attracted attention from researchers. Some conventional controllers have steady-state errors due to modeling errors related to the airframe's inertia and the propeller thrust coefficient. Therefore, this paper proposes a feedforward controller using the airframe's velocity. The proposed controller is verified through simulations and experiments.

In ultra-precision motion systems, vibration has non-negligible influence on motion performance, especially when these systems are getting more lightweight and more flexible. Research on simultaneous optimization of structural and controller design has been conducted to achieve effective vibration control. However, these methods will not have an adequate performance when used in ultra-precision motion systems with a time-varying performance location. In this paper, structural sizes, actuators configuration, and controller parameters are simultaneously optimized. To realize global vibration control and facilitate simultaneous optimization, a new vibration controller with position-dependent control gains is proposed, in which the worst-case vibration magnitude across all considered performance locations is set to be the objective function. To achieve high modeling accuracy, mass and stiffness distribution of actuators is also included into structural dynamics since it plays a large role in structural dynamics. The genetic algorithm is adopted to search for a global optimum. To increase efficiency, R-functions and level-set functions are introduced to translate the complicated over-lapping constraints into a simple integral equality. Neural fitting models instead of the finite element analysis method are used to derive eigenvalues and eigenvectors of the plant. The proposed method is verified on a simplified fine stage in the wafer stage. The numerical results prove its effectiveness.