1. Modern Control Theory(1)- State-space expressions 1. State variables and state space expressions In classical theory, a linear static system can be described by an ordinary differential equation or a transfer function, and a single variable can be used as an output, which may be directly related to the input. 1.1. State variables A set of variables that is sufficient to fully characterize the minimum number of motion states of the system x 1 x n x1···xnx1xn 1.2. State vector Vector consisting of state variables x ( t ) = ( x 1 x n ) x(t) = (x)1 ... xn x (t)=x1xn 1.3. State space It is n-dimensional space composed of state variables as axes 1.4. Equation of state It is a first order differential equations component of the state variable in the system Equation of state of the system using R-L-C network ; Describes the system u u u and x x x The system of first-order differential equations x = Ax + Bu ˙ x = Ax + Bux˙= Ax + Bu 1

2. 1.5. Output equation It is the functional relationship between the output and the state variable, Describe the system y y y and x x x The system of first-order differential equa- tions y = C x + D u y=Cx + Du y= Cx+Du 1.6. State space expression It is a complete dynamical description of a system by combining the equa- tion of state and the output equation x = A x + B u ˙ x = Ax+Bux˙= Ax + Buy = Cx + Duy = Cx + Duy = Cx + D 1.7. System block diagram to express state space It is a block diagram to represent the relationship between system signal transmission for system 2. Scheme of simulation structure for state variables and space ex- pressions The simulation structure diagram is used to reflect the information transfer relationship between the state variables of the system, and the block diagram is used instead of using the detailed simulation diagram of the representative computer, and the number of integrators must be equal to the number of output variables 3. Create state variables and state space expressions One way to create a state space is to create a block diagram of the system and the other is to follow from the physical or derive the chemical mechanism of the system 3.1. Block diagram to create a state space expression It is a method of converting each link of the system into a diagram of a simulated structure 2