scholarly journals Gain-Preserving Data-Driven Approximation of the Koopman Operator and Its Application in Robust Controller Design

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 949
Author(s):  
Keita Hara ◽  
Masaki Inoue
Keyword(s):  
Controller Design ◽  
Internal Model Control ◽  
Feedback Controller ◽  
Data Driven ◽  
Koopman Operator ◽  
Plant System ◽  
Dimensional Approximation ◽  
Model Control ◽  
Data Driven Modeling ◽  
L2 Gain

In this paper, we address the data-driven modeling of a nonlinear dynamical system while incorporating a priori information. The nonlinear system is described using the Koopman operator, which is a linear operator defined on a lifted infinite-dimensional state-space. Assuming that the L2 gain of the system is known, the data-driven finite-dimensional approximation of the operator while preserving information about the gain, namely L2 gain-preserving data-driven modeling, is formulated. Then, its computationally efficient solution method is presented. An application of the modeling method to feedback controller design is also presented. Aiming for robust stabilization using data-driven control under a poor training dataset, we address the following two modeling problems: (1) Forward modeling: the data-driven modeling is applied to the operating data of a plant system to derive the plant model; (2) Backward modeling: L2 gain-preserving data-driven modeling is applied to the same data to derive an inverse model of the plant system. Then, a feedback controller composed of the plant and inverse models is created based on internal model control, and it robustly stabilizes the plant system. A design demonstration of the data-driven controller is provided using a numerical experiment.

Combined Feedforward–Feedback Active Control of Road Noise Inside a Vehicle Cabin

2014 ◽  
Vol 136 (4) ◽  
Author(s):  
Jie Duan ◽  
Mingfeng Li ◽  
Teik C. Lim ◽  
Ming-Ran Lee ◽  
Ming-Te Cheng ◽  
...  
Keyword(s):  
Active Control ◽  
Feedforward Control ◽  
Reference Signal ◽  
Active Noise Control ◽  
Internal Model Control ◽  
Feedback Controller ◽  
Road Noise ◽  
Vehicle Cabin ◽  
Model Control ◽  
Fxlms Algorithm

Conventional active control of road noise inside a vehicle cabin generally uses a pure feedforward control system with the conventional filtered-x least mean square (FXLMS) algorithm. While it can yield satisfactory noise reduction when the reference signal is well correlated with the targeted noise, in practice, it is not always possible to obtain a reference signal that is highly coherent with a broadband response typically seen in road noise. To address this problem, an active noise control (ANC) system with a combined feedforward–feedback controller is proposed to improve the performance of attenuating road noise. To take full advantage of the feedforward control, a subband (SFXLMS) algorithm, which can achieve more noise attenuation over a broad frequency range, is used to replace the conventional FXLMS algorithm. Meanwhile, a feedback controller, based on internal model control (IMC) architecture, is introduced to reduce the road noise components that have strong response but are poorly correlated with the reference signals. The proposed combined feedforward–feedback ANC system has been demonstrated by a simulation model with six reference accelerometers, two control loudspeakers and one error microphone, using actual data measured from a test vehicle. Results show that the performance of the proposed combined controller is significantly better than using either a feedforward controller only or a feedback controller only, and is able to achieve about 4 dBA of overall sound pressure level reduction.

scholarly journals Applied Koopman Theory for Partial Differential Equations and Data-Driven Modeling of Spatio-Temporal Systems

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-16 ◽  
Author(s):  
J. Nathan Kutz ◽  
J. L. Proctor ◽  
S. L. Brunton
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Data Driven ◽  
Nonlinear Pdes ◽  
Dynamic Mode ◽  
Partial Differential ◽  
Koopman Operator ◽  
Dimensional Approximation ◽  
Spatio Temporal ◽  
The Impact

We consider the application of Koopman theory to nonlinear partial differential equations and data-driven spatio-temporal systems. We demonstrate that the observables chosen for constructing the Koopman operator are critical for enabling an accurate approximation to the nonlinear dynamics. If such observables can be found, then the dynamic mode decomposition (DMD) algorithm can be enacted to compute a finite-dimensional approximation of the Koopman operator, including its eigenfunctions, eigenvalues, and Koopman modes. We demonstrate simple rules of thumb for selecting a parsimonious set of observables that can greatly improve the approximation of the Koopman operator. Further, we show that the clear goal in selecting observables is to place the DMD eigenvalues on the imaginary axis, thus giving an objective function for observable selection. Judiciously chosen observables lead to physically interpretable spatio-temporal features of the complex system under consideration and provide a connection to manifold learning methods. Our method provides a valuable intermediate, yet interpretable, approximation to the Koopman operator that lies between the DMD method and the computationally intensive extended DMD (EDMD). We demonstrate the impact of observable selection, including kernel methods, and construction of the Koopman operator on several canonical nonlinear PDEs: Burgers’ equation, the nonlinear Schrödinger equation, the cubic-quintic Ginzburg-Landau equation, and a reaction-diffusion system. These examples serve to highlight the most pressing and critical challenge of Koopman theory: a principled way to select appropriate observables.

Robust Controllers for Pulse-Width-Modulated D.C./D.C. Converters Using Internal-Model-Control Design

1993 ◽  
Vol 207 (3) ◽  
pp. 127-134 ◽  
Author(s):  
D Garabandić ◽  
T Petrović
Keyword(s):  
Model Uncertainty ◽  
Pulse Width ◽  
Internal Model ◽  
Controller Design ◽  
Optimization Method ◽  
Internal Model Control ◽  
Linear Feedback ◽  
Pulse Width Modulated ◽  
Linear Feedback Controller ◽  
Model Control

A linear feedback controller for pulse-width-modulated d.c./d.c. regulator is designed using a frequency domain optimization method based on internal-model-control theory. This method aims to produce suboptimal low-order controllers which are ‘robust’, in the sense that the closed-loop system is guaranteed to meet stability objectives in the presence of model uncertainty. The small-signal model of a d.c./d.c. converter is used for the controller design. The model uncertainty description derived here is based on experiments and non-linear modelling. The result of the synthesis is a family of controllers, and each member of this family satisfies the robust control objectives. All controllers have a multi-loop structure including two feedback loops and one feedforward loop. A detailed design of the controller, including experimental results, is presented.

Multiloop FOPID Controller Design for TITO Process Using Evolutionary Algorithm

2019 ◽  
Vol 8 (3) ◽  
pp. 117-130 ◽  
Author(s):  
Lakshmanaprabu S.K. ◽  
Najumnissa Jamal D. ◽  
Sabura Banu U.
Keyword(s):  
Evolutionary Algorithm ◽  
Pid Controller ◽  
Controller Design ◽  
Search Algorithm ◽  
Bat Algorithm ◽  
Cuckoo Search ◽  
Cuckoo Search Algorithm ◽  
Internal Model Control ◽  
Model Control ◽  
Fractional Order Pid

In this article, the tuning of multiloop Fractional Order PID (FOPID) controller is designed for Two Input Two Output (TITO) processes using an evolutionary algorithm such as the Genetic algorithm (GA), the Cuckoo Search algorithm (CS) and the Bat Algorithm (BA). The control parameters of FOPID are obtained using GA, CS, and BA for minimizing the integral error criteria. The main objective of this article is to compare the performance of the GA, CS, and BA for the multiloop FOPID controller problem. The integer order internal model control based PID (IMC-PID) controller is designed using the GA and the performance of the IMC-PID controller is compared with the FOPID controller scheme. The simulation results confirm that BA offers optimal controller parameter with a minimum value of IAE, ISE, ITAE with faster settling time.

IMC-Based Calibration of the Boost Pressure Controller in an Electrically Assisted Turbocharged Gasoline Engine

2019 ◽  
Author(s):  
Baitao Xiao ◽  
Tyler Kelly ◽  
Timothy Stolzenfeld ◽  
Chenliu Lu ◽  
Dave Bell ◽  
...  
Keyword(s):  
Gasoline Engine ◽  
Pressure Control ◽  
Internal Model Control ◽  
Feedback Controller ◽  
Boost Pressure ◽  
Relay Feedback ◽  
Loop Control ◽  
Electrically Assisted ◽  
Model Control ◽  
Different Types

Abstract In this work, a systematic approach is developed to calibrate a feedback controller for boost pressure control of an electrically assisted turbocharged gasoline engine. The information from the experiments indicates the system can be approximated by a Gain-Integrator-Delay (GID) model which can be robustly identified. Two controllers are designed for two different types of inner loop control (torque/speed) of the electrically assisted turbocharger. The underlying calibration methodology is based on Internal Model Control (IMC). The application of IMC leads to controllers that can be naturally mapped to a classic feedback controller. The plant model is obtained by characterizing the boost system with relay feedback experiments. The calibration methodology as well as the controller designs are demonstrated with a validated simulation platform and good performance is observed.

Improved Internal Model Control-Proportional-Integral- Derivative Fractional-Order Multiloop Controller Design for Non Integer Order Multivariable Systems

2018 ◽  
Vol 141 (1) ◽  
Author(s):  
Tassadit Chekari ◽  
Rachid Mansouri ◽  
Maamar Bettayeb
Keyword(s):  
Fractional Order ◽  
Degrees Of Freedom ◽  
Controller Design ◽  
Mimo Systems ◽  
Design Method ◽  
Internal Model Control ◽  
Tuning Parameter ◽  
Multivariable Systems ◽  
Integer Order ◽  
Model Control

This paper is aimed to propose a multiloop control scheme for fractional order multi-input multi-output (FO-MIMO) systems. It is an extension of the FO-multiloop controller design method developed for integer order multivariable systems to FO-MIMO ones. The interactions among the control loops are considered as disturbances and a two degrees-of-freedom (2DOF) paradigm is used to deal with the process outputs performance and the interactions reduction effect, separately. The proposed controller design method is simple, in relation with the desired closed-loop specifications and a tuning parameter. It presents an interest in controlling complex MIMO systems since fractional order models (FO-models) represent some real processes better than integer order ones and high order systems can be approximated by FO-models. Two examples are considered and compared with other existing methods to evaluate the proposed controller.

Sign in / Sign up

Export Citation Format

Share Document