Inversion-based Feedforward Control Research Articles

System Identification and Two-Degree-of-Freedom Control of Nonlinear, Viscoelastic Tissues.

This paper presents a force control scheme for brief isotonic holds in an isometrically contracted muscle tissue, with minimal overshoot and settling time to measure its shortening velocity, a key parameter of muscle function. A two-degree-of-freedom control configuration, formed by a feedback controller and a feedforward controller, is explored. The feedback controller is a proportional-integral controller and the feedforward controller is designed using the inverse of a control-oriented model of muscle tissue. A generalized linear model and a nonlinear model of muscle tissue are explored using input-output data and system identification techniques. The force control scheme is tested on equine airway smooth muscle and its robustness confirmed with murine flexor digitorum brevis muscle. Performance and repeatability of the force control scheme as well as the number of inputs and level of supervision required from the user were assessed with a series of experiments. The force control scheme was able to fulfill the stated control objectives in most cases, including the requirements for settling time and overshoot. The proposed control scheme is shown to enable automation of force control for characterizing muscle mechanics with minimal user input required. This paper leverages an inversion-based feedforward controller based on a nonlinear physiological model in a system identification context that is superior to classic linear system identification. The control scheme can be used as a steppingstone for generalized control of nonlinear, viscoelastic materials.

Integration of Feedback Control with Feedforward Control for Trajectory Tracking Improvements for Very Fast Microscale Systems

Abstract— This article presents three control schemes: (i) feedback control method using LQR approach, (ii) inversionbased feedforward control method, and (iii) integration of the feedback control method with the feedforward control method, which is a control system that combines a feedback control method with a feedforward approach. Each control scheme is implemented to track two types of desired trajectories: triangle wave trajectory and sawtooth wave trajectory of the same frequency of 200 Hz and the same amplitude of 5 µm. The tracking is challenging in that the system is very fast, and the motion takes microscale amplitudes. The performance of tracking for each control method is evaluated by the quantifying tracking errors. The main contributions of this article are to show that: (i) the feedback control method cannot track the desired trajectories properly, and tracking errors are perhaps not acceptable in some applications, (ii) the feedforward method can substantially improve the performance of tracking as it is compared to that of the feedback approach, and (iii) integration of the feedback control scheme with the feedforward control scheme can further enhance the tracking of the trajectories and can achieve the best performance of tracking. The integration of the feedback control method with the feedforward control method can be effectively used in case good tracking is needed. Keywords— feedback control method, feedforward control method, LQR, reduced order inverse scheme, trajectory tracking, very fast microscale systems

Feedforward and output–feedback control of the cell distribution in chemostat yeast fermentations

A two-degree-of-freedom control strategy is developed and experimentally validated for a set-point change along a desired trajectory of the cell distribution in yeast fermentation. Based on a mathematical model of yeast growth and cell population dynamics, an inversion-based feedforward controller is designed, utilizing a transformation between the biomass concentration and the cell distribution at the equilibrium points. To take disturbances and model inaccuracies into account, the controller is extended by a feedback control law. The controller is applied to a lab-scale stirred tank reactor with Saccharomyces cerevisiae.

Trajectory control of an elastic beam based on port-Hamiltonian numerical models

Abstract We present a systematic approach to realize the precise observer-based trajectory tracking of the tip of a flexible beam using the energy-based port-Hamiltonian (PH) system representation. The first design steps are the structure-preserving spatial discretization by means of a pseudo-spectral method and the structure-preserving order reduction. The model structure is exploited for inversion-based feedforward control, and the control loop is closed via an observer for the friction torque and the state difference. Experimental results for the reference input and the disturbance response illustrate the quality of the design.

Inversion-Based and Optimal Feedforward Control for Population Dynamics With Input Constraints and Self-Competition in Chemostat Reactor Applications

AbstractThrough chemostat reactors, organisms can be observed under laboratory conditions. Hereby, the reactor contains the biomass, whose growth can be controlled via the dilution rate, respectively, the speed of a pump. Due to physical limitations, input constraints need to be considered. The population density in the reactor can be described by a hyperbolic nonlinear integro partial differential equation (IPDE) of first order. The steady-states and generalized eigenvalues and eigenmodes of these IPDE are determined. In order to track a desired reference trajectory, an optimal and an inversion-based feedforward control are designed. For the optimal feedforward control, the singular arc of the control is calculated and a switching strategy is stated, which explicitly considers the input constraints. For the inversion-based feedforward control, the IPDE is first linearized around the steady-state. To comply with the input constraints, a control system simulator is designed. For the simulation model, the IPDE is approximated using Galerkin's method. Simulations show the functionality of the designed controls and provide the basis for comparison. The inversion-based feedforward control operates well near the steady-state, whereas the performance of the optimal feedforward control is not bounded to the proximity to the steady-state.

MIMO multirate feedforward controller design with selection of input multiplicities and intersample behavior analysis

Inversion-based feedforward control is a basic method of tracking controls. The aim of this paper is to design MIMO multirate feedforward controller that improves continuous-time tracking performance in MIMO LTI systems considering not only on-sample but also intersample behavior. Several types of MIMO multirate feedforward controllers are designed and evaluated in terms of the 2-norm of the control inputs. The approach is compared with a conventional MIMO single-rate feedforward controller in simulations. The approach improves the intersample behavior through the optimal selection of input multiplicities with MIMO multirate system inversion.

Spatial-Temporal Trajectory Redesign for Dual-Stage Nanopositioning Systems With Application in AFM

This article focuses on trajectory redesign for dual-stage nanopositioning systems, where speed, range, and resolution are considered. Dual-stage nanopositioning systems are becoming increasingly popular due to their unique ability to achieve long-range and high-speed operation. Conventional trajectory assignment methods for dual-stage systems commonly consider frequency characteristics of the actuators, a process that can inappropriately allocate short-range, low-frequency components of a reference signal. A new systematic range-and-temporal-based trajectory-redesign process is presented, where the desired trajectory is first split based on achievable positioning bandwidth, and then, split spatially based on the achievable range and positioning resolution. Inversion-based feedforward control techniques are then used to compensate for the dynamic and hysteretic behaviors of a piezo-based prototype dual-stage positioner; this control architecture is selected to emphasize improvements achieved through the new trajectory-redesign method, as well as allow for implementation onto platforms with minimal sensing capabilities. Simulations and atomic force microscope experiments are included to demonstrate the success of this redesign procedure compared to approaches that consider frequency or range alone.

Feedforward Control With Disturbance Prediction for Linear Discrete-Time Systems

A typical process control system, in most operations, works to regulate the output against the frequent and variable disturbances, while there is rarely a set-point change. Disturbance rejection solely based on the feedback control tends to be poor when the disturbance propagates to the output quickly. With measurable disturbances, the feedforward control has a great potential for better performance. However, the inversion-based feedforward controller is not realizable if it is noncausal. In this paper, a novel feedforward control scheme is proposed with disturbance prediction capability and yields extraordinary improvement under accurate prediction, but its performance deteriorates with the prediction error. To overcome this, an offsetting mechanism is designed and augmented to the former control for the error compensation. Theoretical analysis and design procedure of the proposed scheme are given. Its effectiveness is demonstrated against the existing feedforward control schemes through simulation on typical examples and a case study on a timing belt actuator.

Linear Time-Variant Vehicle Trajectory Guidance with Nonlinear Inversion-Based Feedforward Control

Abstract This work presents a two-degree-of-freedom (2DOF) control concept for vehicle trajectory guidance for automated driving on highways consisting of a nonlinear feedforward control and a linear time-variant feedback controller. To obtain a linear time-variant system of the error dynamics the nonlinear vehicle model is linearized along a given trajectory. To relieve the feedback controller future knowledge of the vehicle movement contained in the trajectory is used to create a nonlinear inversion-based feedforward control. Finally, the control concept is applied in a sophisticated simulation environment and compared to a nonlinear benchmark controller. In addition, model states are chosen in a way that all required signals can be obtained by state-of-the-art hardware of production vehicles.

Modeling, discretization and motion control of a flexible beam in the port-Hamiltonian framework

In this paper, we present an approach to solve the feedforward motion control problem for a flexible beam, modeled with linear Timoshenko beam theory. The originality lies in the fact that all design steps, from modeling, over discretization to feedforward control are executed within the port-Hamiltonian (PH) framework. To obtain a finite-dimensional PH model which is suitable for inversion-based feedforward control design, a geometric pseudo-spectral discretization is performed. The feedforward control is tested with a plant model implemented in standard FEM software. The results of this paper will be amended by feedback control to achieve highly dynamic motion control on a lab test rig which is currently under construction.

Robust adaptive feedforward output-feedback tracking control for microalgae cultures

A feedforward-feedback control strategy for trajectory tracking of microalgae cultures is developed and experimentally evaluated. On the basis of the Droop model an inversion-based feedforward control is determined, which steers the biomass from given initial to final values in a finite prescribed time. Feedback control is employed for disturbance resilience and improving the stability properties of the desired trajectory. The approach is tested using numerical simulations and experiments in a lab-scale photocatalytic reactor with Chlorella sorokiniana.

Design of an embedded inverse-feedforward biomolecular tracking controller for enzymatic reaction processes.

Feedback control is widely used in chemical engineering to improve the performance and robustness of chemical processes. Feedback controllers require a 'subtractor' that is able to compute the error between the process output and the reference signal. In the case of embedded biomolecular control circuits, subtractors designed using standard chemical reaction network theory can only realise one-sided subtraction, rendering standard controller design approaches inadequate. Here, we show how a biomolecular controller that allows tracking of required changes in the outputs of enzymatic reaction processes can be designed and implemented within the framework of chemical reaction network theory. The controller architecture employs an inversion-based feedforward controller that compensates for the limitations of the one-sided subtractor that generates the error signals for a feedback controller. The proposed approach requires significantly fewer chemical reactions to implement than alternative designs, and should have wide applicability throughout the fields of synthetic biology and biological engineering.

Inversion-based feedforward control design for linear transport systems with spatially acting input

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.

Synergetic repetitive control—a plug-in hybrid control method for precision motion control

Repetitive control is an effective method for reducing periodic errors in motion control applications. However, repetitive control systems are commonly prone to two issues: (1) large transient error during learning cycles and (2) limited ability to deal with complex signals. In this paper, we sought to address both of these concerns by presenting a synergetic repetitive control system comprising proportional-integral-derivative control, repetitive control, and linear plant inversion-based feedforward control to achieve high-performance precision motion control. This study focuses on the synergetic effects of combining these three control actions and compares the resulting performance with a traditional plug-in repetitive control system. Experiment results using a piezoelectric actuator system for the dynamic tracking of complex motion profiles validate the effectiveness of the proposed method.

A Compliant Translational Mechanism Based on Dielectric Elastomer Actuators

This paper reports on a linear actuation mechanism in the form of a parallel-crank mechanism (i.e., double-crank mechanism) articulated with two dielectric elastomer actuators working in parallel that are fabricated as a minimum energy structure. This structure is established by stretching a dielectric elastomer (DE) film (VHB4910) over a polyethylene terephthalate (PET) frame so that the energy released from the stretched DE film is stored in the frame as bending energy. The mechanism can output a translational motion under a driving voltage applied between two electrodes of the DE film. We have proposed visco-elastic models for the DE film and the frame of the actuator so that the mechanical properties of the actuator can more accurately be incorporated into the mechanism model. The proposed model accurately predicts the experimental frequency response of the mechanism at different voltages. In addition, an inversion-based feedforward controller was successfully implemented in order to further validate the proposed model for sensorless position control of the actuators and the parallel-crank mechanism articulated with these actuators.

Multirate-Based Composite Controller Design of Piezoelectric Actuators for High-Bandwidth and Precision Tracking

To track trajectories at rates higher than the resonant frequencies of piezoelectric actuators, this brief presents a comprehensive design method of a multirate-based composite controller consisting of a robust H∞ feedback controller and an inversion-based feedforward controller. The feedback controller is designed for stability and robustness in the presence of disturbances and modeling errors. It is designed for high-bandwidth tracking by reducing phase-lag and gain distortion to overcome the feedback limitation. The proposed composite controller is realized in a piezoelectric stage based on a DSPACE 1104 board. Finally, high-bandwidth and precision tracking are validated in the experimental studies.

Modeling and inverse feedforward control for conducting polymer actuators with hysteresis

Conducting polymer actuators are biocompatible with a small footprint, and operate in air or liquid media under low actuation voltages. This makes them excellent actuators for macro- and micro-manipulation devices, however, their positioning ability or accuracy is adversely affected by their hysteresis non-linearity under open-loop control strategies. In this paper, we establish a hysteresis model for conducting polymer actuators, based on a rate-independent hysteresis model known as the Duhem model. The hysteresis model is experimentally identified and integrated with the linear dynamics of the actuator. This combined model is inverted to control the displacement of the tri-layer actuators considered in this study, without using any external feedback. The inversion requires an inverse hysteresis model which was experimentally identified using an inverse neural network model. Experimental results show that the position tracking errors are reduced by more than 50% when the hysteresis inverse model is incorporated into an inversion-based feedforward controller, indicating the potential of the proposed method in enabling wider use of such smart actuators.

Design, analysis and testing of a parallel-kinematic high-bandwidth XY nanopositioning stage

This paper presents the design, analysis, and testing of a parallel-kinematic high-bandwidth XY nanopositioning stage driven by piezoelectric stack actuators. The stage is designed with two kinematic chains. In each kinematic chain, the end-effector of the stage is connected to the base by two symmetrically distributed flexure modules, respectively. Each flexure module comprises a fixed-fixed beam and a parallelogram flexure serving as two orthogonal prismatic joints. With the purpose to achieve high resonance frequencies of the stage, a novel center-thickened beam which has large stiffness is proposed to act as the fixed-fixed beam. The center-thickened beam also contributes to reducing cross-coupling and restricting parasitic motion. To decouple the motion in two axes totally, a symmetric configuration is adopted for the parallelogram flexures. Based on the analytical models established in static and dynamic analysis, the dimensions of the stage are optimized in order to maximize the first resonance frequency. Then finite element analysis is utilized to validate the design and a prototype of the stage is fabricated for performance tests. According to the results of static and dynamic tests, the resonance frequencies of the developed stage are over 13.6 kHz and the workspace is 11.2 μm × 11.6 μm with the cross-coupling between two axes less than 0.52%. It is clearly demonstrated that the developed stage has high resonance frequencies, a relatively large travel range, and nearly decoupled performance between two axes. For high-speed tracking performance tests, an inversion-based feedforward controller is implemented for the stage to compensate for the positioning errors caused by mechanical vibration. The experimental results show that good tracking performance at high speed is achieved, which validates the effectiveness of the developed stage.

Design and control of a decoupled two degree of freedom translational parallel micro-positioning stage

This paper presents a novel decoupled two degrees of freedom (2-DOF) translational parallel micro-positioning stage. The stage consists of a monolithic compliant mechanism driven by two piezoelectric actuators. The end-effector of the stage is connected to the base by four independent kinematic limbs. Two types of compound flexure module are serially connected to provide 2-DOF for each limb. The compound flexure modules and mirror symmetric distribution of the four limbs significantly reduce the input and output cross couplings and the parasitic motions. Based on the stiffness matrix method, static and dynamic models are constructed and optimal design is performed under certain constraints. The finite element analysis results are then given to validate the design model and a prototype of the XY stage is fabricated for performance tests. Open-loop tests show that maximum static and dynamic cross couplings between the two linear motions are below 0.5% and -45 dB, which are low enough to utilize the single-input-single-out control strategies. Finally, according to the identified dynamic model, an inversion-based feedforward controller in conjunction with a proportional-integral-derivative controller is applied to compensate for the nonlinearities and uncertainties. The experimental results show that good positioning and tracking performances are achieved, which verifies the effectiveness of the proposed mechanism and controller design. The resonant frequencies of the loaded stage at 2 kg and 5 kg are 105 Hz and 68 Hz, respectively. Therefore, the performance of the stage is reasonably good in term of a 200 N load capacity.

Trajectory Tracking of a 3DOF Laboratory Helicopter Under Input and State Constraints

This brief deals with the tracking control design of a helicopter laboratory experimental setup. In order to be able to realize highly dynamic flight maneuvers, both input and state constraints have to be systematically accounted for within the control design procedure. The mathematical model being considered constitutes a nonlinear mathematical mechanical system with two control inputs and three degrees of freedom. The control concept consists of an inversion-based feedforward controller for trajectory tracking and a feedback controller for the trajectory error dynamics. The design of the feedforward controller for a point-to-point flight maneuver is traced back to the solution of a 2-point boundary value problem in the Byrnes-Isidori normal form of the mathematical model. By utilizing special saturation functions, the given constraints in the inputs and states can be systematically incorporated in the overall design process. In order to capture model uncertainties and external disturbance, an optimal state feedback controller is designed on the basis of the model linearization along the desired trajectories. The proposed control scheme is implemented in a real-time environment, and the feasibility and the excellent performance are demonstrated by means of experimental results.