Lecture 02. State space approach. Control system analysis and design. Step1: Modeling By physical laws By identification methods Step2: Analysis Stability, controllability and observability Step3: Control law design Classical, modern and postmodern control Step4: Analysis
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State space approach
Control system analysis and design
Nonlinear Systems by Meiling CHEN 2009
Nonlinear Systems by Meiling CHEN 2009
State equation
Dynamic equation
Output equation
State variable
State space
r input
p output
Nonlinear Systems by Meiling CHEN 2009
Motivation of state space approach
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noise
Example 1
Transfer function
BIBO stable
unstable
Nonlinear Systems by Meiling CHEN 2009
Statespace description
Internal behavior description
Nonlinear Systems by Meiling CHEN 2009
Definition: The stateof a system at time is the amount of information at that together with determines uniquely the behavior of the system for
單純從 並無法決定x在 以後的運動狀況。除非知道 與 。所以 與 是這個系統過去的歷史總結。故 與 可以作為系統的狀態。
Example
M
Nonlinear Systems by Meiling CHEN 2009
Input 對系統的歷史總結。
Example : Capacitor
electric energy
Example : Inductor
Magnetic energy
Nonlinear Systems by Meiling CHEN 2009
Remark 1:狀態的選擇通常與能量有關， 例如:
Position potential energy
Velocity Kinetic energy
Remark 2:狀態的選擇必需是獨立的物理量， 例如:
實際上只有一個狀態變數
Nonlinear Systems by Meiling CHEN 2009
Transfer function
Laplace transform
matrix
Transfer function
Nonlinear Systems by Meiling CHEN 2009
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Remark : the choice of states is not unique.
exist a mapping
Nonlinear Systems by Meiling CHEN 2009
Nonhomogeneous solution
Forced responses
Homogeneous solution
Natural responses
Nonlinear Systems by Meiling CHEN 2009
LTI Dynamic equation
Nonlinear Dynamic equation
Nonlinear Systems by Meiling CHEN 2009