Mathematical control of complex systems

Copyright © 2013 ZidongWang et al.This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited

Inverted pendulum stabilization: Characterization of codimension-three triple zero bifurcation via multiple delayed proportional gains

International audienceThe paper considers the problem of stabilization of systems possessing a multiple zero eigenvalue at the origin. The controller that we propose, uses multiple delayed measurements instead of derivative terms. Doing so, we increase the performances of the closed loop in presence of system uncertainties and/or noisy measurements. The problem formulation and the analysis is presented through a classical engineering problem which is the stabilization of an inverted pendulum on a cart moving horizontally. On one hand, we perform a nonlinear analysis of the center dynamics described by a three dimensional system of ordinary differential equations with a codimension-three triple zero bifurcation. On the other hand, we present the complementary stability analysis of the corresponding linear time invariant system with two delays describing the behavior around the equilibrium. The aim of this analysis is to characterize the possible local bifurcations. Finally, the proposed control scheme is numerically illustrated and discussed

Optimized state feedback regulation of 3DOF helicopter system via extremum seeking

In this paper, an optimized state feedback regulation of a 3 degree of freedom (DOF) helicopter is designed via extremum seeking (ES) technique. Multi-parameter ES is applied to optimize the tracking performance via tuning State Vector Feedback with Integration of the Control Error (SVFBICE). Discrete multivariable version of ES is developed to minimize a cost function that measures the performance of the controller. The cost function is a function of the error between the actual and desired axis positions. The controller parameters are updated online as the optimization takes place. This method significantly decreases the time in obtaining optimal controller parameters. Simulations were conducted for the online optimization under both fixed and varying operating conditions. The results demonstrate the usefulness of using ES for preserving the maximum attainable performance

Control Theory in Engineering

The subject matter of this book ranges from new control design methods to control theory applications in electrical and mechanical engineering and computers. The book covers certain aspects of control theory, including new methodologies, techniques, and applications. It promotes control theory in practical applications of these engineering domains and shows the way to disseminate researchers’ contributions in the field. This project presents applications that improve the properties and performance of control systems in analysis and design using a higher technical level of scientific attainment. The authors have included worked examples and case studies resulting from their research in the field. Readers will benefit from new solutions and answers to questions related to the emerging realm of control theory in engineering applications and its implementation

Synthesis of LQR Controller Based on BAT Algorithm for Furuta Pendulum Stabilization

In this study, a controller design method based on the LQR method and BAT algorithm is presented for the Furuta pendulum stabilization system. Determine the LQR controller, it is often based on the designer's experience or using trial and error to find the Q, R matrices. The BAT search algorithm is based on the characteristics of the bat population in the wild. However, there are advantages to finding multivariate objective functions. The BAT algorithm has an improvement for the LQR controller to optimize the linear square function with fast response time, low energy consumption, overshoot, and a small number of oscillations. Swarm optimization algorithms have advantages in finding global extrema of multivariate functions. Therefore, with a large number of elements of the Q and R matrices, they can also be quickly found and these matrices still satisfy the Riccati equation. The controller with optimal parameters is verified through simulation results with different scenarios. The performance of the proposed controller is compared with a conventional LQR controller and implemented on a real system

Modeling, Reduction, and Control of a Helically Actuated Inertial Soft Robotic Arm via the Koopman Operator

Soft robots promise improved safety and capability over rigid robots when deployed in complex, delicate, and dynamic environments. However, the infinite degrees of freedom and highly nonlinear dynamics of these systems severely complicate their modeling and control. As a step toward addressing this open challenge, we apply the data-driven, Hankel Dynamic Mode Decomposition (HDMD) with time delay observables to the model identification of a highly inertial, helical soft robotic arm with a high number of underactuated degrees of freedom. The resulting model is linear and hence amenable to control via a Linear Quadratic Regulator (LQR). Using our test bed device, a dynamic, lightweight pneumatic fabric arm with an inertial mass at the tip, we show that the combination of HDMD and LQR allows us to command our robot to achieve arbitrary poses using only open loop control. We further show that Koopman spectral analysis gives us a dimensionally reduced basis of modes which decreases computational complexity without sacrificing predictive power.Comment: Submitted to IEEE International Conference on Robotics and Automation, 202