上交自控讲义第二讲.ppt

Module 2 Transfer functions and Block diagram algebra Dynamic system mathematical model Importance Modeling is the foundation of theoretical analysis and compensation for an automatic control system Methodologies Differential / difference equation Transfer function (Laplace transform / Z transform) State-space description Requirements To remember the Laplace transforms of some common components and functions To be capable of drawing block diagrams To grasp Diagram simplifying method To grasp Signal Flow Chart and Mason’s Formula Contents Differential equations of the system Rules for the process Differential equation of an electronic network Differential equation of a DC motor with loads Laplace transforms and inverse transforms Block diagram simplification Transfer function and block diagram Method of direct elimination Block diagram algebra Signal flow chart Mason’s formula Differential equations Rules for the process Analyze the mechanism at work of the system Make out the inputs and outputs of both the entire system and its components Modeling of each component in turn from the system input Simplification according to the required specifications Take Load Effect in account Eliminate middle variables to reach a standard form: Put each system output-related term in the left hand Put each system input-related term in the right hand Put each derivative term in descending order Example 1: An electronic network Apply Kirchholf’s law to the circuit Example 1: An electronic network Eliminate middle variable i1 and i2, From (3), From (2), Take (4), (5) in (1), Example 1: An electronic network Example 2: A DC motor with load Contents Differential equations of the system Rules for the process Differential equation of an electronic network Differential equation of a DC motor with loads Laplace transforms and inverse transforms Block diagram simplification Transfer function and block diagram Method of direct elimination Block diagram algebra Signal flow chart