A method for simplifying linear dynamic systems

Chidambara, M. R.; Davison, E.J.

doi:10.1109/tac.1966.1098264

Cited by 581 publications

(140 citation statements)

References 0 publications

Supporting

Mentioning

123

Contrasting

Unclassified

Order By: Relevance

“…For controller design, this model is further reduced to 24 states using model reduction techniques [31] as compared with 54 states in a full-order model. The retained states correspond to the displacement and velocity on the eighth floor, fifth floor, first floor and base.…”

Section: Active Control: Linear Elastomeric Isolation Systemmentioning

confidence: 99%

“…The retained states correspond to the displacement and velocity on the eighth floor, fifth floor, first floor and base. The reduction is accomplished by constructing a matrix of lower order that has the same dominant eigenvalues and eigenvectors as the original system [31]. The state space equations can be formulated as…”

Section: Active Control: Linear Elastomeric Isolation Systemmentioning

confidence: 99%

“…The H 2 /LQG design is based on a reduced order model [31] that contains 24 states compared with 54 states in the full-order model. The frequency characteristics of the ground excitation are incorporated into the control design through a shaping filter.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Smart base-isolated benchmark building. Part I: problem definition

Narasimhan

Nagarajaiah

Johnson

et al. 2006

Struct. Control Health Monit.

210

181

View full text Add to dashboard Cite

SUMMARYSample controllers for a three-dimensional smart base-isolated building benchmark problem with linear and frictional isolation system are presented in this paper. A Kalman filter is used to estimate the states based on absolute acceleration measurements. Input filters are used to better inform the controller of the spectral content of the earthquake excitations. A reduced order control-oriented model of the benchmark structure with a linear isolation system is developed. A H 2 /linear quadratic Gaussian controller is presented for the active case; additionally, a clipped optimal controller is presented for the semiactive case. A preliminary 'skyhook' semiactive controller is also presented for the benchmark problem. Magnetorheological fluid dampers are used for control in the semiactive case and ideal actuators are used for control in the active case. The focus of this phase I study is on the linear isolation system only. Computed results for the passive, semiactive, and active cases are presented. Detailed comparisons of benchmark performance indices for base-isolated structures with a nominal linear isolation system, with and without control, for a set of strong near-field earthquakes are presented. The modeling and sample control designs demonstrated in this paper can be used to form the basis for studying a wide variety of active and semiactive control strategies}to be developed by the participants in the benchmark study}for linear base-isolated buildings.

show abstract

Section: Active Control: Linear Elastomeric Isolation Systemmentioning

confidence: 99%

Section: Active Control: Linear Elastomeric Isolation Systemmentioning

confidence: 99%

See 1 more Smart Citation

Smart base-isolated benchmark building. Part I: problem definition

Narasimhan

Nagarajaiah

Johnson

et al. 2006

Struct. Control Health Monit.

210

181

View full text Add to dashboard Cite

show abstract

“…Therefore, efforts are made to have a simplified low-order model which retains the dominant characteristics of the original system. During the last four decades, a significant attention has been paid to construct the reduced order model by retaining only a few modes of linear difference system [1][2][3][4] . The appropriate definition and determination as to which state variables significantly participate in the selected modes become very important.…”

Section: Introductionmentioning

confidence: 99%

Designing of PID Controller for Discrete Time Linear System Using Balanced Approach Reduced Order Model

Ravichandran¹,

Rani²,

Manikandan³

2007

American J. of Applied Sciences

View full text Add to dashboard Cite

Abstract:Modeling physical systems usually results in complex high-order dynamic models. It is often desirable to approximate these models by simpler models with reduced order. This study deals with the design of discrete time linear system using a balanced approach reduced order model. The reduced order model retains the desired state variable which contains a significant contribution. A PID controller is designed for the reduced second order model to meet the desired performance specifications by using pole-zero cancellation method. The stabilization of linear discrete time system is achieved by selection of parameters of the PID controller. A numerical example is given to illustrate the design method.

show abstract

“…Thus, the stability requirement of the sliding surface eigenvalues [10] i.e Al contains the r desired eigenvalues.…”

mentioning

confidence: 99%

Sliding mode control design via reduced order model approach

Bandyopadhyay

Abera

Janardhanan

et al. 2007

Int J Automat Comput

View full text Add to dashboard Cite

Abstract-The paper presents the design of sliding modeThe purpose of this paper is to show that sliding mode control for the higher order system via reduced order model. control design can also be done via reduced order model. It It has been shown that a sliding mode control designed for the will be also shown that if a sliding mode control is designed reduced order model gives similar performance for the higher .. r order system. The method has been illustrated by numerical from the reduced order model and lf appled to the higher examples.order system by aggregation, it results in sliding mode motion for the high order system. Index Terms-Sliding mode control, order reduction, con-The brief outline of this paper is as follows: In Section troller simplification II, a brief review on discrete-time sliding mode control is presented. The main result of this paper is included in Section III followed by the illustrative example and simulation results in Section IV. Conclusions are drawn in Section V advantage of the sliding mode control over the other control C strategies is that when the system is confined to the sliding x(k + 1) = TX(k) + FTU(k)(1) manifold, popularly termed as the sliding surface, the system y(k) = Cx(k) is robust, insensitive to parameter uncertainties and external disturbance. The advent of digital computers and samplers in Let, the system be transformed into normal form through a control implementation has broadened the study of discrete-transformation N(k) Tx(k), with the dynamics time systems and the design of control systems in discrete-time. Recently a few researchers have worked on discrete-timesliding mode controller design [4], [5]. In discrete-time sliding mode control, the control input is A. Switching Plane Design calculated once in every sampling interval and is held constant during this period. Due to the finite sampling frequency, it Consider a sliding surface of the form xT = 0 with the may happen in discrete-time sliding mode that the system state sliding function parameter be of form trajectory is unable to move along the sliding surface. It maymove about the sliding surface, thus giving quasi siding mode motion. Regardless of other advantages, the sliding mode The procedure for sliding surface design [8] can be described controller for any system has a complexity proportional to the as follows. number of states in the system. Hence, for a high order system, The system in Eqn. (2) in normal form, when restricted on the sliding mode controller design is also more complicated. the sliding surface CT= 0, would obey the relationship Model order reduction and the reduced order modeling have received considerable attention in the literature in the last thirty years. However a very few research papers are available which where, z2(k) constitutes the last m states of Nk).deal with the controller design via reduced order model [6], Thus, the dynamics of -1 can be represented as [7].

show abstract

A method for simplifying linear dynamic systems

Cited by 581 publications

References 0 publications

Smart base-isolated benchmark building. Part I: problem definition

Smart base-isolated benchmark building. Part I: problem definition

Designing of PID Controller for Discrete Time Linear System Using Balanced Approach Reduced Order Model

Sliding mode control design via reduced order model approach

Contact Info

Product

Resources

About