tailieunhanh - MATHEMATICAL MODELS OF DYNAMIC PHYSICAL SYSTEMS P1

The design of modern control systems relies on the formulation and analysis of mathematical models of dynamic physical systems. This is simply because a model is more accessible to study than the physical system the model represents. | CHAPTER 27__ MATHEMATICAL MODELS OF DYNAMIC PHYSICAL SYSTEMS K. Preston White Jr. Department of Systems Engineering University of Virginia Charlottesville Virginia RATIONALE 795 IDEAL ELEMENTS 796 Physical Variables 796 Power and Energy 797 One-Port Element Laws 798 Multiport Elements 799 SYSTEM STRUCTURE AND INTERCONNECTION LAWS 802 A Simple Example 802 Structure and Graphs 804 System Relations 806 Analogs and Duals 807 STANDARD FORMS FOR LINEAR MODELS 807 I O Form Deriving the I O Form 808 An Example 808 State-Variable Form Deriving the Natural State Variables A 810 Procedure Deriving the Natural State Variables An 811 Example Converting from I O to 812 Phase-Variable Form 812 APPROACHES TO LINEAR SYSTEMS ANALYSIS 813 Transform Methods 813 Transient Analysis Using Transform Methods 818 Response to Periodic Inputs Using Transform Methods 827 STATE-VARIABLE METHODS 829 Solution of the State Equation 829 Eigenstructure 831 SIMULATION 840 Simulation Experimental Analysis of Model Behavior 840 Digital Simulation 841 MODEL CLASSIFICATIONS 846 Stochastic Systems 846 Distributed-Parameter Models 850 Time-Varying Systems 851 Nonlinear Systems 852 Discrete and Hybrid Systems 861 RATIONALE The design of modem control systems relies on the formulation and analysis of mathematical models of dynamic physical systems. This is simply because a model is more accessible to study than the physical system the model represents. Models typically are less costly and less time consuming to construct and test. Changes in the structure of a model are easier to implement and changes in the behavior of a model are easier to isolate and understand. A model often can be used to achieve insight when the corresponding physical system cannot because