Fall 2001 16.311-5 State-Space Approach Basic questions that we will address about the state-space approach What are state-space models? Why should we use them? How are they related to the transfer functions used in classical control design? How do we develop a state-space model? How do we design a controller using a state-space model? ● Bottom line: 1. What: representation of the dynamics of an n n-order system using n first-order differential equations mq+cq+ kq 0 -k/m-c/mq Ax+ Bu 2. Why: State variable form convenient way to work with complex d namics Matrix format easy to use on computers Transfer functions only deal with input/output behavior, but state-space form provides easy access to the "internal" fea- tures/response of the system Allows us to explore new analysis and synthesis tools Great for multiple-input multiple-output systems MIMO) which are very hard to work with using transfer functionsFall 2001 16.31 1—5 State-Space Approach • Basic questions that we will address about the state-space approach: — What are state-space models? — Why should we use them? — How are they related to the transfer functions used in classical control design? — How do we develop a state-space model? — How do we design a controller using a state-space model? • Bottom line: 1. What: representation of the dynamics of an nth-order system using n first-order differential equations: mq¨ + cq˙ + kq = u ⇒    q˙ q¨    =    0 1 −k/m −c/m       q q˙    +    0 1/m    u ⇒ x˙ = Ax + Bu 2. Why: — State variable form convenient way to work with complex dy￾namics. Matrix format easy to use on computers. — Transfer functions only deal with input/output behavior, but state-space form provides easy access to the “internal” fea￾tures/response of the system. — Allows us to explore new analysis and synthesis tools. — Great for multiple-input multiple-output systems (MIMO), which are very hard to work with using transfer functions