Control System Analysis and Design Via the “Second Method” of Lyapunov: I—Continuous-Time Systems

1960 ◽  
Vol 82 (2) ◽  
pp. 371-393 ◽  
Author(s):  
R. E. Kalman ◽  
J. E. Bertram
Keyword(s):  
Control System ◽  
System Analysis ◽  
Transient Behavior ◽  
System Optimization ◽  
Companion Paper ◽  
Analysis And Design ◽  
Continuous Time Systems ◽  
The Subject ◽  
Time Systems ◽  
Second Method Of Lyapunov

The “second method” of Lyapunov is the most general approach currently in the theory of stability of dynamic systems. After a rigorous exposition of the fundamental concepts of this theory, applications are made to (a) stability of linear stationary, linear nonstationary, and nonlinear systems; (b)estimation of transient behavior; (c) control-system optimization; (d) design of relay servos. The discussion is essentially self-contained, with emphasis on the thorough development of the principal ideas and mathematical tools. Only systems governed by differential equations are treated here. Systems governed by difference equations are the subject of a companion paper.

Control System Analysis and Design Via the “Second Method” of Lyapunov: II—Discrete-Time Systems

1960 ◽  
Vol 82 (2) ◽  
pp. 394-400 ◽  
Author(s):  
R. E. Kalman ◽  
J. E. Bertram
Keyword(s):  
Discrete Time ◽  
Continuous Time ◽  
System Analysis ◽  
Companion Paper ◽  
Data Systems ◽  
Sampled Data ◽  
Analysis And Design ◽  
Continuous Time Systems ◽  
Time Systems ◽  
Second Method Of Lyapunov

The second method of Lyapunov is applied to the study of discrete-time (sampled-data) systems. With minor variations, the discussion parallels that of the companion paper on continuous-time systems. Theorems are stated in full but motivation, proofs, examples, and so on, are given only when they differ materially from their counterparts in the continuous-time case.

scholarly journals Comparative study of zero effects in pole-placement control system design via the shift and delta transforms

2005 ◽  
Vol 18 (3) ◽  
pp. 439-451
Author(s):  
Milica Naumovic
Keyword(s):  
Control System ◽  
System Design ◽  
Pole Placement ◽  
Control System Design ◽  
Single Input Single Output ◽  
Single Output ◽  
Continuous Time Systems ◽  
Single Input ◽  
Pole Placement Control ◽  
Time Systems

This paper deals with the special replacement of the shift operator and its associated z transform by delta operator and ? transform, respectively. The aim of the paper is to clarify the role of zeros of discretized linear single input single output continuous-time systems modeled by shift and delta operators. In particular, the effect of zero dynamics on the control system design based on classical pole-zero assignment in the case of both operators is considered. The analysis is illustrated by simulation results.

Study on the Cooling Water Systems with Multiple Cooling Water Supplies

2012 ◽  
Vol 610-613 ◽  
pp. 2497-2500
Author(s):  
Yong Guo ◽  
Zhi Yong Liu
Keyword(s):  
Water Reuse ◽  
System Analysis ◽  
Cooling Water ◽  
System Optimization ◽  
Water Systems ◽  
Heat Transfer Process ◽  
Water Supplies ◽  
Pinch Point ◽  
Analysis And Design ◽  
Water Pinch

Water pinch technology is a process integration technology used for enterprises water system optimization, in order to improve the water reuse rate. Application of water pinch point technology to the whole system analysis and design, to establish a feasible performance index, and then determine the detailed process of design and transformation to achieve the predetermined target performance. This paper presents a technique for simultaneous targeting and design in cooling water systems comprising of at least two cooling towers and several cooling water using operations. Through comprehensive analysis on the cooling water systems with multiple cooling water supplies, determine the corresponding heat transfer process to the cooling tower, obtained better results than literature.

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