Lecture #10 State space approach
State equation Dynamic equation Output equation State variable State space r- input p- output Meiling CHEN
Inner state variables C A D B + - Meiling CHEN
Motivation of state space approach Example 1 + - noise Transfer function BIBO stable unstable Meiling CHEN
BIBO stable, pole-zero cancellation Example 2 BIBO stable, pole-zero cancellation -2 + - Meiling CHEN
State-space description Internal behavior description then system stable State-space description Internal behavior description Meiling CHEN
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。 Definition: The state of a system at time is the amount of information at that together with determines uniquely the behavior of the system for Example M 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。 Meiling CHEN
Example : Capacitor electric energy Input 對系統的歷史總結。 Example : Inductor Magnetic energy Meiling CHEN
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 Meiling CHEN
Example K M2 M1 B1 B3 B2 Meiling CHEN
Example Armature circuit Field circuit Meiling CHEN
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Dynamical equation Transfer function matrix Transfer function Laplace transform matrix Transfer function Meiling CHEN
Example MIMO system Transfer function Meiling CHEN
Remark : the choice of states is not unique. + - exist a mapping Meiling CHEN
Different state equation description p is nonsingular Meiling CHEN
Definition : Two dynamical systems with are said to be equivalent. The nonsingular matrix p is called an equivalence transformation. & Theorem: two equivalent dynamical system have the same transfer function. Meiling CHEN