DYNAMICS and CONTROL

Transcription

1 DYNAMICS and CONTROL MODULE 1I (1I) Models of Systems & Signals Analogies Presented by Pedro Albertos Professor of Systems Engineering and Control - UPV 1

2 Modules: Examples of systems and signals Models of systems and signals Representations Analogies Formalism Controlled systems: properties Control systems design Control benefits Topics to study 2

3 SIGNALS Systems and Models SYSTEM SYSTEM: Set of interconnected elements with time varying magnitudes, some of them being accessible, and with some manipulated variables, in general. 3

4 Autonomous systems SOLAR SYSTEM SYSTEM: Set of heavenly bodies with a time varying position, providing some information but without any option to be manipulated. 4

5 Forced system Electric Oven Commands Door Food Fan Temperature Lights 5

6 Forced system: Model Electric Oven Commands Door Food Fan Temperatures Lights Supplied heat= Transferred heat+ Absorbed heat MODEL: Partial representation Balances 6

7 Temperature Forced system: Model Commands OVEN Door Food Supplied heat= Transferred heat+ Absorbed heat MODEL: Balances Processes Heat transmission 7

8 Forced system Water tank: Taps Orifices Tank dimensions Water level Outlet speed Water ph Temperature 8

9 Water level Forced system: Model Water level (mm) Tap flow TANK Orifice Dimensions Constants Time (sec) Inlet water flow= Retained flow+ Outlet water flow Balances MODEL: Processes Hydraulic systems 9

10 Velocity Forced system: Model Voltage MOTOR Friction Constant Brake/Load Variable Motor torque = Acceleration torque+ Friction torque+ Load torque Balances MODEL: Processes Electromecanic systems 10

11 Velocity Forced system: Model Axis speed (rpm) Voltage MOTOR Friction Brake/Load Constant Variable Time (sec) Motor torque = Acceleration torque+ Friction torque+ Load torque Balances MODEL: Processes Electromecanic systems 10

12 Output: y(k) Computer sequence Input Const. ALGORITHM y(0) = 25; For k=1 until k=100 y(k+1)=0.95*y(k)+10; Represent y(k) MODEL: y(k+1) = 0.95*y(k) + u(k); u(k) = 10; y(0) = 25 11

13 Analogies Oven Tank Motor Algorithm Processes: Hydraulic Traffic Communications Flows: Water Vehicles Information MODEL: Mathematical representation Output= Operator x Input 12

14 Models Mathematical representation Systems: Signal processor Signal generator y( s) G( s). u( s) Output= Operator x Input Output= Operator x Initial conditions 13

15 What have we seen today? Systems models and analogies System: Information processor Signals attached to a system Internal and external Manipulated/Disturbance Measurable (outputs) Representation Analogy Function 14

16 What is next? Modules: Examples of systems and signals Models of systems and signals Representations Analogies Formalism Controlled systems: properties Control systems design Control benefits Topics to study 15

17 Thank you! The sources of some of these figures are : Slide Por Jo Teichmann, Augsburg, Germany (KUKA Roboter GmbH) [Public domain], undefined Slide10 Por Jo Teichmann, Augsburg, Germany (KUKA Roboter GmbH) [Public domain], undefined 16