北航自控原理课件3(英文版).ppt

Set t=0,we have so We define is a n×n matrix, called matrix exponential. Therefore the solution of homogeneous equation is To solve by Laplace transform, we get The inverse Laplace transform of x(s),that is: So Therefore we have: * Difference between classical control theory and modern control theory Analysis Numerical value Make experiments Result is not a unique The characteristic of design Algebra Matrix theory Differential and integral Complex functions The basics of math State-equations Transfer functions models All systems SISO,time-invariant system Plant(process) Modern control theory Classical control theory Chapter 3 State Variable Model (1)The state equation State vector System matrix Input matrix Control signal State variables (2)Output equation Output vector Output matrix Dynamic equation State: The state of a system is a set of variables such that the knowledge of these variables and the input functions will, with the equations describing the dynamics,provide the future state and output of the system. State variables: The state variable describe the future response of a system.given the present state, the excitation inputs, and the equations describing the dynamics. State vector:The set of state variables represents the elements or components of the n state vector ; that is, 3.1 The state variable of a dynamic system State space: The state space is defined as the n-dimensional space in which the components of the n state vector represent its coordinate axes. State equation: The state equations of a system are a set of n first- order differential equations, where n is the number of independent states. Example: A spring-mass-damper system u(t) y k b M The differential equation describes the behavior of the system can be written When we define a set of state variable Therefore we can write the differential equations as two first-order equations: The set of s