Optimal Feedforward Control Research Articles

Optimal feedforward compensators for systems with right-half plane zeros

Feedforward from measurable disturbances is a powerful complement to feedback control to improve disturbance rejection capability. Recent works have remarked the necessity of a design strategy for those cases where the ideal feedforward controller is not realizable. In this paper, a simple shaping design procedure is presented together with straightforward rules to obtain optimal feedforward controllers for the case when the ideal compensator is not realizable due to right-half plane zeros in the process dynamics. Finally, some simulations and a robustness analysis demonstrate the benefits of the proposed tuning rules.

Optimal LQ feedforward tracking with preview: Practical design for rigid body motion control

For reference-tracking motion control, preview-based linear quadratic (LQ) design methods provide an effective means to balance tracking performance with available actuation capacity. This paper considers a control structure for which the optimal feedforward controller is independent of the feedback controller. In this way, explicit implementation formulas for feedforward controllers are derived that can be applied to a range of rigid-body motion systems. Key aspects of the optimal LQ solutions are identified, particularly how the choice of design weightings affect steady-state error for polynomial tracking. A redesign procedure for finite preview-time is proposed that preserves exact polynomial tracking properties and control bandwidth of the optimal solutions. Comparative experimental results are presented for a motor-driven linear motion stage.

Robust Two Degree-Of-Freedom Control for MIMO System with Both Model and Signal Uncertainties

In the study, a model inversion based two degree-of-freedom (DOF) controller is proposed to achieve optimal robust performance for multi-input-multi-output (MIMO) system with existence of both model and signal uncertainties. The original plant dynamics are modified by a pre-compensator and a post-compensator to obtain a diagonally dominant matrix, where the selected dynamics of the plant are contained within the diagonal entries. The inversion of the diagonal matrix, as a result, reflects the inversion of the plant dynamics within a specified frequency range. The feedback controller is designed using a standard H2 mixed sensitivity approach. The feedforward controller consists of plant inversion and a feedforward filter, which is optimized to balance the trade-off between nominal performance and robust performance under model uncertainty and signal uncertainty. A numerical example is used to demonstrate the improvement of the robust performance when using the optimal feedforward control.

Modeling and Control for Max-Plus Systems with Partial Synchronization

A max-plus system with partial synchronization is a persistent discrete event system divided into a main subsystem and a secondary subsystem where some events in the secondary subsystem can only occur when (not after) associated events in the main subsystem occur. A formal model based on max-plus recursive equations is presented for max-plus systems with partial synchronization. Furthermore, the control problem of output tracking is addressed by assigning a higher priority to the main subsystem: the performance of the main subsystem is never degraded to improve the performance of the secondary subsystem. Two different control approaches are investigated: optimal feedforward control and model predictive control. In both cases, residuation theory is applied to efficiently solve the optimization problem.

Quasi optimal feedforward control of a very low frequency high-voltage test system

Abstract This paper presents the design of a quasi optimal feedforward controller for a new type of high-voltage test systems. Compared to existing solutions, this test system has the advantage of a compact lightweight construction and is thus particularly suitable for on-site tests. For system analysis and controller design, a tailored mathematical model is derived, which describes the (slow) envelope dynamics of the occurring amplitude modulated signals. The proposed (quasi optimal) control concept ensures a simultaneous minimization of the mean power losses and of the distortion of the output voltage. Simulation results for a validated mathematical model show the feasibility of the approach.

Optimal feedforward control with a parametric structure applied to a wafer stage

To meet the ever-increasing requirements for accurate manufacturing equipment, feedforward control has been widely regarded as an effective method. A nominal feedforward controller equals to the inverse model, which conventional model-based approaches could not acquire accurately due to the inevitable model error, the stability of the inverse model and so on. Therefore, a data-based feedforward control based on a parametric structure is proposed. The structure takes acceleration and snap set-points as signal inputs and both paths equip finite impulse response filters. Each finite impulse response filter is parameterized by a series of coefficients, assuming that the difference between the actual output and nominal output is an affine function of these coefficients. The coefficients are obtained from a gradient and Hessian approximation–based algorithm and optimized by minimizing a quadratic objective function. Two methods are proposed to approximate the gradient: the direct approach and the Toeplitz matrix approach. Finally, the proposed algorithm is assessed on a developed wafer stage. The results show that the proposed parametric structure improves the scanning tracking performance and provides a more desirable way to deal with the model with several resonances in low frequency.

Robust delay-dependent feedforward control of neutral time-delay systems via dynamic IQCs

This paper studies the design problem of delay-dependent based robust and optimal feedforward controller design for a class of time-delay control systems having state, control and neutral type delays which are subject to norm-bounded uncertainties and type measurable or observable disturbance signals. Two independent loops which include state-feedback and dynamic feedforward controller form the basis of the proposed control scheme in this study. State-feedback controller is generally used in stabilisation of the nominal delay-free system, whereas the feedforward controller is used for improving disturbance attenuation performance of the overall system. In order to obtain less conservative results, the delay and parametric uncertainty effects are treated in operator view point and represented by frequency-dependent (dynamic) integral quadratic constraints (IQCs). Moreover, sufficient delay-dependent criterion is developed in terms of linear matrix inequalities (LMIs) such that the time-delay system having parametric uncertainties is guaranteed to be asymptotically stable with minimum achievable disturbance attenuation level. Plenty of numerical examples are provided at the end, in order to illustrate the efficiency of the proposed technique. The achieved results on minimum achievable disturbance attenuation level and maximum allowable delay bounds are exhibited to be less conservative in comparison to those of controllers having only feedback loop.

Two-time dimensional dynamic matrix control for batch processes with convergence analysis against the 2D interval uncertainty

A batch process can be treated as a 2-dimentional (2D) system with a time dimension within each batch and a batch dimension from batch to batch. This paper integrates the learning ability of iterative learning control (ILC) into the prediction model of model predictive control (MPC). Based on this integrated model, a 2D dynamic matrix control (2D-DMC) algorithm with a feedback control and an optimal feed-forward control is proposed. The sufficient conditions for exponentially asymptotic and monotonic convergence of the proposed 2D-DMC are established with proof under certain assumptions, in the presence of not only the completely repeatable uncertainties but also the non-repeatable interval uncertainties. The effectiveness of the proposed control scheme is tested through simulation and experimental implementation in the context of injection molding, a typical batch process. The results show that the batch process control performance is significantly improved.

Design of Optimal Low-Order Feedforward Controllers

Design rules for optimal feedforward controllers with lead-lag structure in the presence of measurable disturbances are presented. The design rules are based on stable first-order models with time delays, FOTD, and are optimal in the sense of minimizing the integrated***squared error. The rules are derived for an open-loop setting, considering a step disturbance. This paper also discusses a general feedforward structure, which enables decoupling in the design of feedback and feedforward controllers, and justifies the open-loop setting.

Delay-Dependent Feedforward Control of Uncertain Neutral Time-Delay Systems via Dynamic IQCs

This paper deals with the design problem of a delay-dependent ℋ∞ based robust optimal feedforward controller for a class of time-delay control systems having state delays, control delays and neutral delays when the system is subject to norm bounded uncertainties. The proposed scheme in this study is formed by two independent loops which include state-feedback and dynamic feedforward controller. The delay and parametric uncertainty effects are represented by dynamic Integral Quadratic Constraints (IQCs). Furthermore, sufficient delay-dependent criteria is developed in terms of Linear Matrix Inequalities (LMIs) such that the time-delay system with parametric uncertainty is guaranteed to be asymptotically stable with a minimum disturbance attenuation level. The achieved results on the minimum allowable disturbance attenuation level in the provided numerical examples are exhibited to be less conservative in comparison to those of controllers having only feedback loop.

Notions of local controllability and optimal feedforward control for quantum systems

Local controllability is an essential concept for regulation and control of time-varying nonlinear dynamical systems; in the classical control logic it is at the foundation of neighboring optimal feedback and feedforward control. We introduce notions of local controllability suited to feedforward control of classical input disturbances in bilinear quantum systems evolving on projective spaces and Lie groups. Tests for local controllability based on a Gramian matrix analogous to the nonlinear local controllability Gramian, which allow assessment of which trajectories can be regulated by perturbative feedforward in the presence of classical input noise, are presented. These notions explicitly incorporate system bilinearity and the geometry of quantum states into the definition of local controllability of quantum systems. Associated feedforward strategies are described.

Spatiotemporal dynamics and feedforward control of an infinite-dimensional, time-variant, thermal-coating process

In this contribution, a model for the spatiotemporal dynamics of a thermal-coating process is derived from first principles (the conservation of energy). The model is a dynamical system consisting of a system of hyperbolic, partial differential equations (PDEs), describing the evolution of the temperature distribution of the substrate. By studying the C 0- semigroup generated by the system operator we find that in discrete time the infinite-dimensional plant may conveniently be represented by finite-dimensional operators defined on appropriately chosen Euclidean spaces. This representation provides the basis for numerical efficient solution of several optimal feedforward control problems associated with set point changes and launching of the process. Numerical and experimental studies highlight the value of this approach.

Feedforward model predictive control of a non-linear solar collector plant with varying delays

This study discusses non-linear optimal feedforward control of solar collector plants. The control problem is challenging, with non-linear disturbance effects and long input-dependent transport delays. The controller operates in a model-based predictive control framework, without feedback and constraints, to highlight feedforward controller performance gains. To reduce the computational complexity state extension is avoided when modelling the time delays. The motivation for this is provided by a proof of the equivalence between state extension and direct prediction in optimal control, for non-linear multiple-input-multiple-output (MIMO) systems with time delays in disturbances and controls. The solar collector controller also uses flow-dependent sampling to reduce the time variation of the delays. To obtain an accurate model for feedforward controller design, a black-box recursive prediction error identification algorithm was used for modelling of the non-linear plant using measured data. Experimentally, accurate feedforward control was obtained when the controller design was tested with simulation, using measured disturbances from the plant. About two-thirds of the control effort needed appears to be available by feedforward control only. In order to evaluate the algorithms in difficult conditions, the evaluation was performed on data obtained during a day with partly cloudy weather. This caused large flow variations, and consequently large time delay variations.

An optimal feedforward control design for the set-point following of MIMO processes

In this paper we propose a new methodology for the design of a feedforward action for the improvement of the set-point following performance of feedback controlled square MIMO processes. In particular, by exploiting an analytical decoupling technique, the feedforward signals are determined in order to achieve predefined output transition times, by assuming that the transfer function matrix of the system consists of first order plus dead time transfer functions. An analytical expression of the feedforward signal is derived and this allows to solve easily a multiobjective optimisation problem in order to minimise the transition time of each output subject to constraints of the actuators. Simulation as well as experimental results demonstrate the effectiveness of the method.

Relative Motion Estimation and Control Strategy for a Spacecraft to an Uncooperative Object

In this paper, a control strategy for a spacecraft (“Pursuer”) to rendezvous with an uncooperative object (“Target”) is dealt with. This strategy consists of a feedforward optimal control phase (phase 1) and a feedback control phases (phase 2 and 3). In the feedforward optimal control phase, the target's future attitude motion is predicted from the result of motion estimation using image data in order to determine the final state for the maneuver. It is expected that there will be errors in the result of motion estimation for the target and error compensation is expected to be necessary. For this purpose, the pursuer estimates and predicts target's motion during maneuver, and recomputes the optimal control input using it. A quasi-optimal control input is proposed and named “Adjusted Control Input” in order to adapt this error compensation. And its performance is investigated through a numerical simulation of the pursuer's position control.

Flow stabilisation by Dirichlet boundary control

AbstractRe–attachment of separated flow is investigated for the model problem of a backward facing step at moderate Reynolds number (up to 400), where the length of the detachment zone is reduced by blowing in (or sucking out) fluid through a nozzle below the step. Both optimal feed forward control as well as a simple feedback control are considered, with surprisingly good results obtained by a very simple (non–optimal) linear feedback controller. Numerical results are shown. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Optimal approach to and alignment with a rotating rigid body for capture

This paper addresses a feed-forward optimal control problem for one rigid body to approach to and align with another arbitrarily rotating rigid body, with an application to the satellite rendezvous problem. In particular, we focus on the satellite rendezvous strategy of finding an optimal trajectory, and the required thrust force profiles, which will guide the chasing spacecraft to approach the tumbling satellite such that the two vehicles will eventually have no relative rotation and thus a subsequent docking or capture operation can be safely performed with a normal docking or capture mechanism. Our approach is to model the system using rigid-body dynamics and apply Pontryagin’s Maximum Principle for the optimal control. A planar problem is presented as a case study, in which together with the Maximum Principle, the Lie algebras associated with the system are used to examine the existence of singular extremals for the time-optimal control problem. Also, optimal trajectories and the corresponding set of control force/torque profiles are numerically generated for the time/fuel-consumption optimal control problem.

Optimal Feed-Forward Control for Multizone Baking in Microlithography

An algorithm for feed-forward control to improve the performance of a multizone baking system used for lithography in semiconductor manufacturing is derived in this paper. It uses linear programming optimization of the heat transfer in a multizone bake plate to produce a predetermined heating sequence. The objective is to minimize the temperature disturbance induced by the placement of a wafer at ambient temperature on the hot multizone bake plate, and the improvement is verified experimentally.

CRITERIA AND TIME HORIZON IN FEEDFORWARD MPC FOR NON-LINEAR SYSTEMS WITH TIME DELAYS

During feedforward control experiments with a non-linear solar cooling plant with long transport delays, it was observed that a conventional selection of criterion for MPC did result in too poor performance. A reason for the inaccurate control is explained and it is shown how a modified choice of time horizon may improve performance. The paper also compares two discrete time optimal feedforward control problems for nonlinear systems with time delays. A formulation where the time delay is incorporated in the state vector using one state variable for each sampling period is compared to a formulation where a predicted output is used directly in the criterion function. Provided that the criterion functions are selected in certain ways, the equivalence between the two problems is proved. Avoiding a state vector extension implies a substantial computational complexity reduction for systems with long time delays.

Infinite non-causality in active cancellation of random noise

Active cancellation of broadband random noise requires the detection of the incoming noise with some time advance. In an duct for example this advance must be larger than the delays in the secondary path from the control source to the error sensor. In this paper it is shown that, in some cases, the advance required for perfect noise cancellation is theoretically infinite because the inverse of the secondary path, which is required for control, can include an infinite non-causal response. This is shown to be the result of two mechanisms: in the single-channel case (one control source and one error sensor), this can arise because of strong echoes in the control path. In the multi-channel case this can arise even in free field simply because of an unfortunate placing of sensors and actuators. In the present paper optimal feedforward control is derived through analytical and numerical computations, in the time and frequency domains. It is shown that, in practice, the advance required for significant noise attenuation can be much larger than the secondary path delays. Practical rules are also suggested in order to prevent infinite non-causality from appearing.