Elec321 Dorf and Bishop 2011 Modern control systems/ sections 2.6 and 2.9
Use the Laplace transforms to develop block diagram models
Use the Laplace transforms to develop signal-flow graph modelsThe dynamic systems that comprise automatic control systems are represented mathematically by a set of simultaneous differential equations. The Laplace transformation reduces the problem to the solution of a set of linear algebraic equations. Since control systems are concerned with the control of specific variables the controlled variables must relate to the controlling variables. This relationship is typically represented by the transfer function of the subsystem relating the input and output variables. Therefore one can correctly assume that the transfer function is an important relation for control engineering.
The importance of this cause-and-effect relationship is evidenced by the facility to represent the relationship of system variables by diagrammatic means. The block diagram representation of the system relationships is prevalent in control system engineering. Block diagrams consist of unidirectional operational blocks that represent the transfer function of the variables of interest.
How do we use Laplace transforms to develop block diagram models for physical systems? How do we use Laplace transforms to develop signal-flow graph models for physical systems?