Design of reduced-order feedforward controller

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.

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.

There exist a direct and an indirect methods in designing reduced-order H/sub /spl infin// controller. The former method is difficult and there exists no effective way presently. The latter method has been used conventionally. However, the resultant controller may be conservative. We propose a method of designing a less conservative reduced-order controller by using genetic algorithm (GA). Since it is difficult to search reduced-order controller directly, we search for the full-order controller whose reduced-order controller has approximate performance of the optimal full-order H/sub /spl infin// controller. Then, it is reduced by the reduction technique. In order to search the desired full-order controller effectively, Glover's parameterization is applied. Furthermore, we propose the coding which searches only optimal full-order controllers, since the desired full-order controller is expected to be one of numerous optimal full-order controllers. In order to show the effectiveness of the proposed method, an numerical example is given.

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.

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

We propose a method to design reduced-order output-feedback controllers for fluid flows with the use of data produced by full-order controllers. First, the full-order controller is obtained by combining an ensemble Kalman filter (EnKF) and a model predictive controller (MPC) that are designed based on the Navier–Stokes equations. The full-order controller has high computational complexity and, therefore, is not suitable for real-time implementation. Hence, we use the full-order controller in offline numerical simulations to generate data for data-driven design of the reduced-order controller with low computational complexity. We find a reduced-order subspace of a closed-loop system under the full-order control from the data. This subspace underlies the reduced-order output-feedback controller. The reduced-order state-feedback law is obtained by approximating the full-order MPC with the use of its input/output data. The reduced-order observer is designed for a reduced-order model that is derived by using the Gaussian process regression (GPR). The GPR enables us to design the reduced-order observer which can evaluate uncertainty due to state-dependent residuals of the reduced-order model. We demonstrate the proposed method for a control problem of a flow around a cylinder at the Reynolds number 100. Numerical simulations reveal that the reduced-order controller performs as almost well as the full-order controller for a set of initial states. In addition, robustness of the reduced-order controller to a temporal disturbance that is not considered in the control design is confirmed in the simulations.

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.

In this paper, the feedforward controller design problem for high-precision electromechanical servo systems that execute finite time tasks is addressed. The presented procedure combines the selection of the fixed structure of the feedforward controller and the optimization of the controller parameters by iterative trials. A linear parametrization of the feedforward controller in a two-degree-of-freedom control architecture is chosen, which results in a feedforward controller that is applicable to a class of motion profiles as well as in a convex optimization problem, with the objective function being a quadratic function of the tracking error. Optimization by iterative trials avoids the need for detailed knowledge of the plant, achieves the controller parameter values that are optimal with respect to the actual plant, and allows for the adaptation to possible variations that occur in the plant dynamics. Experimental results on a high-precision wafer stage and a desktop printer illustrate the procedure.

Kalman state estimator for aircraft structural load alleviation using eigenpair assignment

The problem of feed-forward control of overhead crane system is discussed. By combining the Kalman's controllability theory and Hartman-Grobman theorem from dynamical system theory, a linear, continuous state feedback-based feed-forward controller that stabilizes the crane system at the desired end position of payload is designed. The efficacy of proposed controller is demonstrated by comparing the simulation experiment results for overhead crane with/without time-varying length of hoisting rope.

Adding feedforward controllers to feedback-only control systems can often improve the transient response performance. In the literature several architectures have been proposed, which combine feedback and feedforward controls together, such as Feedforward Closed-Loop Inverse (FFCLI) and Feedforward Plant Inverse (FFPI). In this paper, we investigate discrete-time feedforward control designs and show how some designs lead to large intersample ripple in the response of the continuous-time plant that is being controlled. If the feedforward controller cancels high frequency zeros with small damping factors in the discretized plant, large intersample ripple can result. Ignoring such zeros in the feedforward controller will suppress intersample ripple significantly, while slightly slowing the response. In this work, this phenomenon is demonstrated with a second-order plant and a fourth-order Torsional Disk System (TDS) plant.

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.

This paper presents a method for designing a controller that achieves the best positioning performance while maximizing the energy efficiency of a redundantly actuated hybrid feed drive. A two-degree-of-freedom controller, consisting of a feedforward (FF) controller for tracking and a feedback (FB) controller for regulation, is assumed. It is shown that the ideal FF controller, which achieves perfect tracking with maximum efficiency, is not always stable. Therefore, a method for designing a stable FF controller that achieves perfect tracking with near optimal efficiency is proposed. Furthermore, the optimal relationship between FB control inputs, which guarantees maximum efficiency for any specified regulation performance, is derived. Two approaches for using the derived optimal relationship to synthesize a FB controller that achieves the best positioning performance while maximizing efficiency are proposed. Simulations and machining experiments are conducted to demonstrate the effectiveness of the proposed energy-efficient FF and FB controller design methods. Significant improvements in energy efficiency (without sacrificing positioning performance) are reported.

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.

This paper concerns reduced-order stable controllers in a unified way for two typical examples of underactuated robots called the Acrobot and the Pendubot which are two-link planar robots moving in a vertical plane with a single actuator at joints 1 and 2, respectively. The main contributions of this paper are threefold. First, using properties of the mechanical parameters of two-link planar robots, this paper proves via a constructive procedure that stable controllers exist for a local stabilization of the upright equilibrium point (two links are in upright position) of each robot by designing a specific output with an adjustable parameter and employing the pole-zero relation of the linearized model around the equilibrium point. Second, the paper presents a design method to obtain explicitly a formula of second-order (reduced-order) stable controllers by choosing the adjustable parameter. Third, in terms of strong stabilization (stabilization with a stable controller), some new features of the Acrobot and the Pendubot are revealed and are compared with those of the cart-pendulum system. Simulation results for the two robots are presented to validate the theoretical results.