Operator-based Control Research Articles

Koopman Operator Based Predictive Control With a Data Archive of Observables

Abstract The control of complex systems is often challenging due to high-dimensional nonlinear models, unmodeled phenomena, and parameter uncertainty. The increasing ubiquity of sensors measuring such systems and increased computational resources has led to an interest in purely data-driven control methods, particularly using the Koopman operator. In this paper, we elucidate the construction of a linear predictor based on a sequence of time realizations of observables drawn from a data archive of different trajectories combined with subspace identification methods for linear systems. This approach is free of any predefined set of basis functions but instead depends on the time realization of these basis functions. The prediction and control are demonstrated with examples. The basis functions can be constructed using time-delayed coordinates of the outputs, enabling the application to purely data-driven systems. The paper thus shows the link between Koopman operator-based control methods and classical subspace identification methods. The approach in this paper can be extended to adaptive online learning and control.

Operator-based nonlinear fault detection and fault tolerant control for microreactor using one-class SVM

This paper proposes a method of nonlinear fault detection scheme using one-class support vector machine (SVM) and operator-based fault tolerant control system for a microreactor with Peltier device. This method requires only one-shot training data for the normal condition of the plant. The data is used to learn for the SVM, it realises nonlinear fault detection without the known fault condition of the plant. Also, the control system that consists of the nonlinear model of the microreactor system and operator-based controller designed by the model is introduced as the fault tolerant control system using compensation operator to remove the sensor fault. The usefulness of the method is shown by an experiment of the temperature sensor fault case for the temperature control system of the microreactor system.

Data-Driven Model Predictive Control using Interpolated Koopman Generators

In recent years, the success of the Koopman operator in dynamical systems analysis has also fueled the development of Koopman operator-based control frameworks. In order to preserve the relatively low data requirements for an approximation via Dynamic Mode Decomposition, a quantization approach was recently proposed in [Peitz \& Klus, Automatica 106, 2019]. This way, control of nonlinear dynamical systems can be realized by means of switched systems techniques, using only a finite set of autonomous Koopman operator-based reduced models. These individual systems can be approximated very efficiently from data. The main idea is to transform a control system into a set of autonomous systems for which the optimal switching sequence has to be computed. In this article, we extend these results to continuous control inputs using relaxation. This way, we combine the advantages of the data efficiency of approximating a finite set of autonomous systems with continuous controls. We show that when using the Koopman generator, this relaxation --- realized by linear interpolation between two operators --- does not introduce any error for control affine systems. This allows us to control high-dimensional nonlinear systems using bilinear, low-dimensional surrogate models. The efficiency of the proposed approach is demonstrated using several examples with increasing complexity, from the Duffing oscillator to the chaotic fluidic pinball.

Operator-based nonlinear fault detection and fault tolerant control for microreactor using one-class SVM

This paper proposes a method of nonlinear fault detection scheme using one-class support vector machine (SVM) and operator-based fault tolerant control system for a microreactor with Peltier device. This method requires only one-shot training data for the normal condition of the plant. The data is used to learn for the SVM, it realises nonlinear fault detection without the known fault condition of the plant. Also, the control system that consists of the nonlinear model of the microreactor system and operator-based controller designed by the model is introduced as the fault tolerant control system using compensation operator to remove the sensor fault. The usefulness of the method is shown by an experiment of the temperature sensor fault case for the temperature control system of the microreactor system.

Operator-Based Control System Analysis and Design for Nonlinear System with Input and Output Constraints

Smart material-based actuators and sensors have been widely used in practice owing to their various advantages. However, in the working process of these actuators and sensors, their output responses always deduce non-smooth nonlinear constraints. The constraint resulting from the actuator is called the input constraint and the constraint caused by the sensor is called the output constraint. These input and output constraints may induce inaccuracies and oscillations, severely degrading system performance. Therefore, the input and output constraints brought about by actuators and sensors should be considered in control system design. In this paper, system analysis for a nonlinear system with input and output constraints will be considered. The effect from the input constraint to the internal signal in the control system will be discussed. Moreover, the influence of the output constraint on the whole system will be studied. Further, the sufficient conditions for maintaining the stability of the system are obtained. Then, by using the robust right coprime factorization approach, an operator-based internal model like control structure is proposed for mitigating the input and output constraints. Finally, the effectiveness of the proposed design scheme will be confirmed through numerical simulation.

An Operator-based Nonlinear Vibration Control System Using a Flexible Arm with Shape Memory Alloy

In the past, arms used in the fields of industry and robotics have been designed not to vibrate by increasing their mass and stiffness. The weight of arms has tended to be reduced to improve speed of operation, and decrease the cost of their production. Since the weight saving makes the arms lose their stiffness and therefore vibrate more easily, the vibration suppression control is needed for realizing the above purpose. Incidentally, the use of various smart materials in actuators has grown. In particular, a shape memory alloy (SMA) is applied widely and has several advantages: light weight, large displacement by temperature change, and large force to mass ratio. However, the SMA actuators possess hysteresis nonlinearity between their own temperature and displacement obtained by the temperature. The hysteretic behavior of the SMA actuators affects their control performance. In previous research, an operator-based control system including a hysteresis compensator has been proposed. The vibration of a flexible arm is dealt with as the controlled object; one end of the arm is clamped and the other end is free. The effectiveness of the hysteresis compensator has been confirmed by simulations and experiments. Nevertheless, the feedback signal of the previous designed system has increased exponentially. It is difficult to use the system in the long-term because of the phenomenon. Additionally, the SMA actuator generates and radiates heat because electric current passing through the SMA actuator provides heat, and strain on the SMA actuator is generated. With long-time use of the SMA actuator, the environmental temperature around the SMA actuator varies through radiation of the heat. There exists a risk that the ambient temperature change dealt with as disturbance affects the temperature and strain of the SMA actuator. In this research, a design method of the operator-based control system is proposed considering the long-term use of the system. In the method, the hysteresis characteristics of the SMA actuator and the temperature change around the actuator are considered. The effectiveness of the proposed method is verified by simulations and experiments.

Digital controller based on delta operator for high‐frequency DC–DC switching converters

Both the stability and the control accuracy of digital controllers for DC-DC switching converters utilising shift operators severely degrade under high switching frequencies. This study presents a digital-proportion integration differentiation (D-PID) controller based on a delta operator for DC-DC converters with high switching frequencies. Both the stability and the control accuracy of the digitally controlled converters were effectively improved when using the delta operator instead of the shift operator. The hardware cost and the processing speed requirements were also considerably reduced. The performance advantages of such a D-PID controller were theoretically analysed, and then simulated using the Simulink platform. Finally, both the proposed D-PID controller and a conventional shift operator-based controller were implemented for DC-DC switching converters on a field-programmable gate array (FPGA) platform. The benefits of using the delta operator over the shift operator were experimentally verified, and the test results indicated that for the DC-DC switching converter with 2 MHz switching frequency, better control accuracy can be obtained by using the delta operator than using the shift operator.

Experimental study on operator-based robust nonlinear vibration control for an L-shaped arm with unknown load

A linear-motor-driven L-shaped arm experimental system is studied in this article. The arm with unknown load is driven by the motor and actuated by a piezoelectric actuator at the same time. This study aims to control the motor motion and the actuator’s behavior simultaneously, resulting in less arm vibration. First, the arm vibration relating to the load and the linear motor is modeled by considering it as an Euler–Bernoulli beam. Then, the control design for the arm and motor is proposed using the operator-based nonlinear control approach involving an on-line discrete wavelet transform. The operator-based right coprime factorization is used to ensure the system stable and robust. The discrete wavelet transform is utilized to remove the influences of some undesired disturbances and improve the operator-based control performance. In addition, the load mass is estimated using fast Fourier transform based on the discrete wavelet transform decomposed vibration signal. Finally, experiments are conducted comparing with the previous study, and the results show that the proposed control is effective to reduce the arm vibration in less time.

Robust Stability and Tracking for Operator-Based Nonlinear Uncertain Systems

In this paper, operator-based robust control for nonlinear uncertain system is considered by using robust right coprime factorization approach. In details, the effects from uncertainties for nonlinear uncertain systems are analyzed through internally stable control design. For the stabilizing system, an internal model control (IMC) like operator-based control design is proposed. Based on the proposed design scheme, the effect from uncertainties is eliminated. By using operator theory-based approach, the system is robustly stable and the desired tracking performance can be realized. Finally, the effectiveness of the proposed design scheme is demonstrated by a simulation example. Note to Practitioners-Robust stability and tracking problems are two well-known topics in the field of control, which play an important role in real application and attract the researchers' attention all the time. Especially, these issues on nonlinear systems still remain challenging owing to complexity and the nonlinear characteristic property. Another challenging issue in nonlinear control is the effects from uncertainties. Motivated by these issues, robust control design by using operator theoretic-based approach has caused for concern owing to its effectiveness in dealing with nonlinearity and uncertainties. This paper provides a survey of the research in the above issues that would help practitioners in controlling nonlinear uncertain systems and in understanding the advantages of operator-based approach.

Nonlinear Perfect Tracking Control for a Robot Arm with Uncertainties Using Operator-Based Robust Right Coprime Factorization Approach

<div class=""abs_img""><img src=""[disp_template_path]/JRM/abst-image/00270001/06.jpg"" width=""300"" />Plant uncertainties compensation</div> In this paper, a robust nonlinear perfect tracking control for a robot arm with uncertainties is proposed by using operator-based robust right coprime factorization approach. In general, there exist unknown modelling errors in measuring structural parameters of the robot arm and external disturbances in real situations. In the present control system design, the effect of the modelling errors and disturbances on the system performance is considered to be uncertainties of the robot arm dynamics. Considering the uncertainties, a robust nonlinear perfect tracking control using operator-based robust right coprime factorization is investigated. That is, first, considering the unknown uncertain plant generates limitations in obtaining the so-called universal stability and tracking conditions, the effect of uncertain plant is compensated by designed operator-based feedback control scheme. Second, a new perfect tracking condition is proposed for improving the trajectory of the robot arm. Finally, the effectiveness of the designed system is confirmed by simulation results. </span>

Implementing home energy management system with UPnP and mobile applications

The power grid is undergoing a revolution and modernization through integrating information and communication technologies with the power system and also installing new electricity system technologies. Distributed controls in a certain self-reliant power-service area are critical means to modernize the power system to be the Smart Grid. Since the self-reliant area is assumed to perform physical and/or expert-engineered operations that should be integrated, monitored and controlled by a computational cyber system, the area is one area where the cyber and physical systems interact together, and home in the Smart Grid is one example for the area. In this paper, we propose a home energy management system (HEMS) to realize full automation combining computational and physical systems in a home area, which excludes operator-based control and management. The proposed system is designed to be built on the Universal Plug-and-Play architecture, and it can be accessed remotely over the Internet via mobile applications that work in Apple iPhone. Based on the design, we actually implemented the HEMS and constructed an empirical testbed that consists of networked personal computers, home appliances, and portable wireless devices. With the empirical testbed, we verified the monitoring and controlling functions of the HEMS. Additionally we carried out an extensive simulation study with the measured data of power consumption and the collected data of power price in order to see the effectiveness of the proposed HEMS. We also discuss about some limitations and challenges that we have encountered in designing and implementing the HEMS.

Operator-based non-linear control system design for unstable plants with input saturation

Operator-based robust right coprime factorisation approach is an interesting approach for non-linear control. It provides an effective framework for non-linear unstable system. In practice, the input constraint always exists, which induces that the real control input is different from the controller output, thus the input constraint may destabilise the system. However, control system design for non-linear plants with input saturation has seldom been studied due to the difficulties in dealing with non-linearity. Also in operator-based robust right coprime factorisation method, input saturation is not considered. In this paper, a new control system design for non-linear unstable plants with input saturation is proposed. Based on the robust right coprime factorisation, an operator-based switching controller is designed, which avoids the unstable region. Moreover, based on the proposed design scheme, the output tracking performance is also realised, and the effectiveness of the proposed method is verified by simulation.

Networked non-linear control for an aluminum plate thermal process with time-delays

This article considers networked non-linear control for an aluminum plate thermal process. This is done by using operator-based robust right coprime factorisation approach and Bezout identity to guarantee robust stable networked control system, as well as an operator-based tracking controller to ensure the controlled process output tracking the desired reference input. An experimental result is given for the case of temperature control of the aluminum plate thermal process.