The N finite steps linear quadratic Gaussian control algorithm

Active vibration control systems are commonly reported to be the most robust and effective method for vibration control of structures. However, the type of ground motions and the type of analysis may greatly influence their performances. This study investigates the seismic response of building with and without an active controller under pulse-type ground motions. A 20-story non-linear steel benchmark building is considered. Linear and non-linear analysis is conducted to check the effectiveness of the active control system. Active control with a linear quadratic Gaussian (LQG) control algorithm is applied to the benchmark building for seismic control purposes. Initially, some ground motions are selected following earlier studies from the literature concerning the benchmark building. It is found that the LQG control algorithm is quite effective under the considered earthquakes, and the analysis type does not affect the effectiveness of the controller. Thereafter, a set of additional 69 pulse-type ground motions are considered to check the performance of the LQG control algorithm and to find the suitability of linear analysis. It is noticed that under such pulse-type ground motion, the LQG control algorithm is not much effective if the non-linear behavior of the structure is incorporated in the seismic analysis, whereas in case of linear analysis, the LQG control algorithm is still effective. It is concluded that neglecting the non-linear behavior may lead to unconservative estimates of the seismic response when performing seismic analysis and designing structures equipped with active vibration control systems.

This paper presents an integrated passive-active (i.e. hybrid) system for seismic response control of a cable-stayed bridge. Since multiple control devices are operating, a hybrid control system could alleviate some of the restrictions and limitations that exist when each system is acting alone. Lead rubber bearings are used as passive control devices to reduce the earthquake-induced forces in the bridge and hydraulic actuators are used as active control devices to further reduce the bridge responses, especially deck displacements. In the proposed hybrid control system, a linear quadratic Gaussian control algorithm is adopted as a primary controller. In addition, a secondary bang-bang type (i.e. on-off type) controller according to the responses of lead rubber bearings is considered to increase the controller robustness. Numerical simulation results show that control performances of the integrated passive-active control system are superior to those of the passive control system and are slightly better than those of the fully active control system. Furthermore, it is verified that the hybrid control system with a bang-bang type controller is more robust for stiffness perturbation than the active controller with a μ-synthesis method, and there are no signs of instability in the over-all system whereas the active control system with linear quadratic Gaussian algorithm shows instabilities in the perturbed system. Therefore, the proposed hybrid protective system could effectively be used for seismically excited cable-stayed bridges.

New adaptive robust [formula omitted] control of smart structures using synchrosqueezed wavelet transform and recursive least-squares algorithm

This paper presents the problem definition and guidelines of a set of benchmark control problems for seismically excited nonlinear buildings. Focusing on three typical steel structures, 3-, 9-, and 20-story buildings designed for the SAC project for the Los Angeles, California region, the goal of this study is to provide a clear basis to evaluate the efficacy of various structural control strategies. A nonlinear evaluation model has been developed that portrays the salient features of the structural system. Evaluation criteria and control constraints are presented for the design problems. The task of each participant in this benchmark study is to define (including sensors and control algorithms), evaluate, and report on their proposed control strategies. These strategies may be either passive, active, semiactive, or a combination thereof. The benchmark control problems will then facilitate direct comparison of the relative merits of the various control strategies. To illustrate some of the design challenges, a sample control strategy employing active control with a linear quadratic Gaussian control algorithm is applied to the 20-story building.

This thesis document outlines the development of a multibody dynamics simulation of an actively stabilized multiple-input, multiple-output, coupled, balancing cube and the process of verifying the results by implementing the control algorithm in hardware. A non-linear simulation of the system was created in Simscape and used to develop a Linear Quadratic Gaussian control algorithm. To implement this algorithm in actual hardware, the system was first designed, manufactured, and assembled. The structure of the cube and the reaction wheels were milled from aluminum. DC brushless motors were installed into the mechanical system. In terms of electronics, a processor, orientation sensor, motor drivers, analog to digital converters, and a pulse width modulation board were assembled into the cube. Upon completion, the software to control the cube was developed using Simulink and run on a Raspberry Pi computer within the mechanism.

In this study, a frequency-dependent algorithm is proposed in independent modal space as an improvement to the linear quadratic Gaussian (LQG) control algorithm. The passive control parameters such as mass, stiffness and damping of a dynamic system are sensitive to different frequency ratios when subjected to external excitation. Depending upon the sensitivity of these parameters, the algorithm is developed in such a way that a response reduction similar to that of an LQG algorithm can be achieved with a significantly smaller control force. An effective gain is obtained by optimizing the H2 norm of the transfer function. It is observed from the results that the algorithm works well for high frequency ratio and near resonance regimes. Thus, a combination of the LQG and the proposed algorithms is considered as a modified LQG control algorithm, where the effectiveness of both algorithms is utilized. The efficiency of the modified LQG control algorithm is demonstrated by considering a base-isolated structure when subjected to earthquake base excitations. By comparing with the results it is observed that the modified LQG control algorithm is more efficient in terms of response reduction with a much lower control force as compared to the LQG control algorithm. It is envisioned that the modified LQG control algorithm will be highly useful for response control of base-isolated structures.

Combined iterative learning and delta-operator adaptive linear quadratic Gaussian control of a commercial rapid thermal processing system

Multi-objective genetic algorithms for cost-effective distributions of actuators and sensors in large structures

The study of this paper focuses on smart isolation structure, a method for realizing structural vibration control by using Simulink simulation is proposed according to the proposed sequential optimal control algorithm. In the Simulink simulation environment, A smart isolation structure is used to compare the control effect of three algorithms, i.e., classical optimal control algorithm, linear quadratic gaussian control algorithm and sequential optimal control algorithm under the condition of sensor contaminated with noise. Simulation results show that this method can be applied to the simulation of sequential optimal control algorithm and the proposed sequential optimal control algorithm has a good ability of resisting the noise and better control efficiency.

Combining the approaches of optimal control theory and linear prediction technique, the user's transmitting powers are minimized and the system capacity is maximized with the quality of services (QoS) being satisfied simultaneously for all mobile terminals. A linear quadratic form of power control problem in wideband code division multiple access (WCDMA) systems is established and the fading channel path-gain is predicted. Simulation results show graphically that the proposed predictive linear quadratic power control (PLQ-PC) algorithm converges faster no less than 7 percents and makes the system support about 1.2 times users compared with those obtained by auto-tuning fuzzy power control (ATF-PC) and signal-interference ratio based power control (SIR-PC) algorithms, respectively.

An efficient vibration control can reduce negative effects induced by environmental vibrations and thereby improve the performance of precision instruments and the qualities of manufacture. The performance of the widely used linear quadratic regulator control algorithm, a classical active control methodology, depends on the parameters of the control algorithm. Consequently, a set of fixed parameters cannot satisfy the demand for controlling various types of environmental vibrations. Therefore, this study proposes a vibration identification method based on a convolutional neural network. This method helps to optimize the linear quadratic regulator algorithm by selecting corresponding optimal parameters according to the identification results, thereby achieving the objective of optimal control subjected to various types of vibration inputs. Specifically, environmental vibration signals are collected, and the preliminary features of the vibrations (i.e. wavelet coefficient matrices or images) are adopted as input samples for the convolutional neural network. A genetic algorithm is used to optimize the parameters of the linear quadratic regulator algorithm for each type of vibration; subsequently, the trained convolutional neural network model with the best performance is used to identify the vibration and select the corresponding optimal parameters of the linear quadratic regulator algorithm under different types of vibration inputs. Case studies show that the performance of the improved linear quadratic regulator control method is significantly better than that of the conventional linear quadratic regulator algorithm with fixed parameters.

A controller is developed by combining the extended linear quadratic matrix control (EQDMC) and neural network algorithms. The dynamic neural network scheme is used to identify the process and generate a nonlinear model. The control algorithm is applied to a multi-input multi-output (MIMO) evaporative cooling KCl-NaCl-H2O crystallizer. Closed loop responses of the system using the proposed algorithm and those of PID controllers are compared. It is shown that in all cases, the response of the proposed controller to step changes in setpoints is faster than the PID controllers.

In this paper, a mathematical model of flight pattern and flight attitude is established and analyzed. The flight pattern of the power patrol flight is analyzed. Based on the original linear quadratic optimal control algorithm, the motion and optimal control model of the unmanned aerial vehicle (UAV) patrol process is established to meet the unmanned aerial vehicle (UAV) inspection constraints, then a linear quadratic optimization Control based optimal control algorithm is proposed. In this paper, four-rotor aircraft as an example for simulation research, different motion models with different optimization control, and add different interference signals and the corresponding filter algorithm for antijamming performance testing. The simulation results show that the UAV can obtain good control effect by the linear quadratic optimal control, and its stability and anti - jamming performance can be improved obviously.

Matrix quadratic equation solution derivation applied in finding steady state solutions of Riccati differential equations with constant coefficients

Previous article Next article Conditions for Positive and Nonnegative Definiteness in Terms of PseudoinversesArthur AlbertArthur Alberthttps://doi.org/10.1137/0117041PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Richard Bellman, Introduction to matrix analysis, McGraw-Hill Book Co., Inc., New York, 1960xx+328 MR0122820 0124.01001 Google Scholar[2] A. Ben-Israel and , A. Charnes, Contributions to the theory of generalized inverses, J. Soc. Indust. Appl. Math., 11 (1963), 667–699 10.1137/0111051 MR0179192 0116.32202 LinkISIGoogle Scholar[3] T. N. E. Greville, Some applications of the pseudoinverse of a matrix, SIAM Rev., 2 (1960), 15–22 10.1137/1002004 MR0110185 0168.13303 LinkISIGoogle Scholar[4] Charles A. Rohde, Generalized inverses of partitioned matrices, J. Soc. Indust. Appl. Math., 13 (1965), 1033–1035 10.1137/0113070 MR0190161 0145.03801 LinkISIGoogle Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Error Analysis of Multirate Leapfrog-Type Methods for Second-Order Semilinear OdesConstantin Carle and Marlis HochbruckSIAM Journal on Numerical Analysis, Vol. 60, No. 5 | 13 October 2022AbstractPDF (1129 KB)The truncated moment problem on the union of parallel linesLinear Algebra and its Applications, Vol. 649 | 1 Sep 2022 Cross Ref On the non-symmetric semidefinite Procrustes problemLinear Algebra and its Applications, Vol. 648 | 1 Sep 2022 Cross Ref Dynamic discrete-time portfolio selection for defined contribution pension funds with inflation riskJournal of Industrial & Management Optimization, Vol. 18, No. 1 | 1 Jan 2022 Cross Ref Stability and Functional Superconvergence of Narrow-Stencil Second-Derivative Generalized Summation-By-Parts DiscretizationsJournal of Scientific Computing, Vol. 90, No. 1 | 10 December 2021 Cross 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