Nonlinear feedforward control of chemical reactors

A steady-state nonlinear feedforward controller (FFC) for measurable disturbances is designed for a continuous bioreactor, which is represented by Hammerstein type nonlinear model wherein the nonlinearity is a polynomial with input multiplicities. The manipulated variable is the feed substrate concentration (Sf) and the disturbance variable is the dilution rate (D). The productivity (Q=DP) is considered as the controlled variable. The desired value of Q=3.73 gives two values of feed substrate concentration. The nonlinearity in the gain is considered for relating output to the manipulated variable and separately for the relation between output to disturbance variable. The FFC is also designed for the overall linearized system. The performance of the FFC is evaluated on the nonlinear differential equation model. The FFC is also designed for the model based on a single nonlinear steady-state equation containing both D and Sf. This nonlinear FFC gives the best performance. The nonlinear FFC is also designed by using only linear gain for the disturbance and nonlinear gain for the manipulated variable. Similarly, nonlinear FFC is also designed by using linear gain for the manipulated variable and the nonlinear gain for the disturbance variable. The performances of these FFC schemes are compared.

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.

Controlling nonlinear dynamics arises in various engineering fields. We present efforts to model the forced van der Pol system control using physics-informed neural networks (PINN) compared to benchmark methods, including idealized nonlinear feedforward (FF) control, linearized feedback control (FB), and feedforward-plus-feedback combined (C). The aim is to implement circular trajectories in the state space of the van der Pol system. A designed benchmark problem is used for testing the behavioral differences of the disparate controllers and then investigating controlled schemes and systems of various extents of nonlinearities. All methods exhibit a short initialization accompanying arbitrary initialization points. The feedforward control successfully converges to the desired trajectory, and PINN executes good controls with higher stochasticity observed for higher-order terms based on the phase portraits. In contrast, linearized feedback control and combined feed-forward plus feedback failed. Varying trajectory amplitudes revealed that feed-forward, linearized feedback control, and combined feed-forward plus feedback control all fail for unity nonlinear damping gain. Traditional control methods display a robust fluctuation for higher-order terms. For some various nonlinearities, PINN failed to implement the desired trajectory instead of becoming “trapped” in the phase of small radius, yet idealized nonlinear feedforward successfully implemented controls. PINN generally exhibits lower relative errors for varying targeted trajectories. However, PINN also shows evidently higher computational burden compared with traditional control theory methods, with at least more than 30 times longer control time compared with benchmark idealized nonlinear feed-forward control. This manuscript proposes a comprehensive comparative study for future controller employment considering deterministic and machine learning approaches.

10 - Concepts and applications of feedforward control

Tubular chemical reactor are units frequently used in chemical and biochemical industry. From the system theory point of view, tubular chemical reactors belong to a class of nonlinear distributed parameter systems. Their mathematical models are described by sets of nonlinear partial differential equations (PDR). The methods of modelling and simulation of such processes are described eg. in (Luyben 1989; Ingham et al. 1994; Severance 2001; Babu 2004). Relations between process behaviour and their control methods can be found in (Seborg et al. 1989; Ogunnaike and Ray 1994; Marlin 1995; Corriou 2004). It is well known that the control of chemical reactors, and, tubular reactors especially, often represents very complex problem. The control problems are due to the process nonlinearity, its distributed nature, and high sensitivity of the state and output variables to input changes. In addition, the dynamic characteristics may exhibit a varying sign of the gain in various operating points, the time delay as well as non-minimum phase behaviour. Evidently, the process with such properties is hardly controllable by conventional control methods, and, its effective control requires application some of advanced methods (e. g. Adaptive Control, Predictive Control, Robust Control or any others). However, at all events, a previous analysis of the process behaviour is obligatory. The paper presents all mathematical models used for simulations of both steady-state and dynamic charakteristics of the tubular chemical reactor together with results of some simulations. The combinations of observed variables are chosen in accordance with purposes of prospective control design. MODEL OF THE PLANT

This work presents the results from a field test of LIDAR assisted collective pitch control using a scanning LIDAR device installed on the nacelle of a mid-scale research turbine. A nonlinear feedforward controller is extended by an adaptive filter to remove all uncorrelated frequencies of the wind speed measurement to avoid unnecessary control action. Positive effects on the rotor speed regulation as well as on tower, blade and shaft loads have been observed in the case that the previous measured correlation and timing between the wind preview and the turbine reaction are accomplish. The feedforward controller had negative impact, when the LIDAR measurement was disturbed by obstacles in front of the turbine. This work proves, that LIDAR is valuable tool for wind turbine control not only in simulations but also under real conditions. Furthermore, the paper shows that further understanding of the relationship between the wind measurement and the turbine reaction is crucial to improve LIDAR assisted control of wind turbines.

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.

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.

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.

Modeling the effect of wall capacitance on the dynamics of an exothermic reaction system in a batch reactor

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.

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.

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

During recent years there has been considerable interest in using bilinear systems [1, 2] as mathematical models to represent the dynamic behavior of a wide class of engineering, biological and economic systems. Moreover, there are some methods [3] which may approximate nonlinear control systems by bilinear systems. For the first time Zubov has proposed a method of stabilization control synthesis for a set of programmed motions in linear systems [4]. In papers [5, 6] this method has been developed and used to solve the same problem for bilinear systems.In the present paper the following problems are considered. First, synthesis of nonlinear control as feedback under which the bilinear control system has a given set of programmed and asymptotic stable motions. Because this control is not unique, the second problem concerns optimal stabilization. In this paper a method for the design of nonlinear optimal control is suggested. This control is constructed in the form of a convergent series. The theorem on the sufficient conditions to solve this problem is represented.

To improve the shift quality of vehicle with clutch-to-clutch gear shifts, a nonlinear controller based on flatness is proposed for the clutch slip control during the inertia phase. A nonlinear feedforward control is designed in consideration of the system nonlinearities, and a linear feedback control is given to accommodate the model errors and the disturbances. The proposed control scheme has small computational demand and the complex nonlinear characteristics of powertrain system appear in their original form of lookup tables. Finally, the designed controller is tested on an AMESim powertrain simulation model, which contains a time-variant model of clutch actuators.