Control System A combination of components acting together to perform a specific objective. Disdurbance INPUT System OUTPUT 日96
Control System • A combination of components acting together to perform a specific objective
Control System Examples Temperature control of the passenger compartment of a car Passenger Desired compartment temperature Heater or temperature Controller air Passenger (Input) conditioner compartment (Output) Sensor
Control System Examples • Temperature control of the passenger compartment of a car
Dynamic Control Example Control example:Temperature control of a room What need regulate: Room temperature Device used to influence the output: Heater/AC Desirable behavior:Room temperature follows the set term even under uncertainties/disturbances. Disturbance Set temperature Heater/AC (e.g.,people,sun) (26 degrees C) controller Plant Room (room Temp) temperature
Dynamic Control Example Control example: Temperature control of a room What need regulate: Room temperature Device used to influence the output: Heater/AC controller Plant (room Temp) Room temperature Set temperature Heater/AC (26 degrees C) Desirable behavior: Room temperature follows the set term even under uncertainties/disturbances. Disturbance (e.g., people, sun)
Linear and Nonlinear System Definition of Linear system: Definition of Nonlinear Coefficients of terms(including system: dependent variable and its derivatives)are constants or dx functions of time. -2 +10x=0 dt ·Classification linear,time-varying differential equation; d2x +10x=0 linear,time-invariant +(1-c0s21) dt differential equation. d2x +5 +10x=0 dt2 dt
Linear and Nonlinear System • Definition of Linear system: Coefficients of terms (including dependent variable and its derivatives) are constants or functions of time. • Classification linear, time-varying differential equation; linear, time-invariant differential equation. 1 cos 2 10 0 2 2 x dt dx t dt d x （ － ） 5 10 0 2 2 x dt dx dt d x • Definition of Nonlinear system: 1 cos 2 10 0 2 2 x dt dx x dt d x （ － ）
Properties of Linear System 1.Superposition叠加性 x (t) Linear system y,(t) 2.Homogeneity齐次性 x2(t) Linear +y2(t) system x(t)+x2(t) Linear y(t)+y2(t) system Linear Bx (1) system
Properties of Linear System 1. Superposition 叠加性 2. Homogeneity 齐次性 ( ) 2 x t ( ) 1 ( ) y t 1 x t Linear system Linear system ( ) 2 y t x ( t ) x ( t ) 1 ＋ 2 Linear system y ( t ) y ( t ) 1 2 ( ) 1 x t Linear system ( ) 1 y t