PLANT DESCRIPTION use virtual or soft sensors, based on a identified - PDF document

METTI5 Spring School – Tutorial 7 June 2011 METTI 5 Spring School – T7 – S. Malan & C. Greco 1 METTI 5 Spring School – T7 – S. Malan & C. Greco 2 Outline TUTORIAL 7 - REAL DATA • Introduction IDENTIFICATION OF AN • Plant description ACTUAL RADIATOR-ROOM • Models choice: SSV models; I/O models • Experimental setup and data SYSTEM AIMED TO VIRTUAL • Estimation method: Operational aspects; Software tools SENSOR DESIGN • Identification and validation results Stefano Malan & Cosimo Greco • Virtual sensors: State space solution; Input output solution Dip. di Automatica e Informatica • Matlab scripts Politecnico di Torino METTI5 Spring School – T7 – S. Malan & C. Greco 3 METTI5 Spring School – T7 – S. Malan & C. Greco 4 Introduction Many reasons drives to energy management and saving in buildings INTRODUCTION • Reduce pollution (respect protocols target) • Reduce operating costs • Maximize user comfort • Fairly rearrange cost distribution on actual consumption: right accounting • Give a sense of responsibility to final user • Create and maximize final user’s energy awareness • ... METTI5 Spring School – T7 – S. Malan & C. Greco 5 METTI5 Spring School – T7 – S. Malan & C. Greco 6 Introduction Reduce monitoring and right accounting costs and complexity: PLANT DESCRIPTION • use virtual or soft sensors, based on a identified model, to substitute actual sensors First step to design a Virtual Sensor: • identify a suitable mathematical model of the system able to provide, as an output, the signal to be measured: open loop VS Second step to design a Virtual Sensor: • use Control Theory to design a closed loop VS S. Malan & C. Greco - Politecnico di Torino 1

METTI5 Spring School – Tutorial 7 June 2011 METTI5 Spring School – T7 – S. Malan & C. Greco 7 METTI5 Spring School – T7 – S. Malan & C. Greco 8 Plant description Plant description • University office room, 12 square meters Research aim: • Heating system: radiator connected to central heating unit • set up a methodology for micro-accounting heating • Input water temperature: set by the central heating unit energy consumption • Water flow: can be regulated by means of a valve EXTERNAL • reduce the need of physical sensors → virtual sensor N WINDOW • 3 measurements needed to compute Heating Power: water flow 𝑅 Radiatore 1. RADIATOR water input temperature 𝑈 𝑛 𝑄 ℎ = 𝑅𝜍𝑑 𝑈 𝑛 − 𝑈 ROOM UNDER 2. 𝑠 STUDY water output temperature 𝑈 3. 𝑠 • tutorial aim: CORRIDOR identify a model of the overall radiator-room system to suitably design a temperature 𝑈 𝑠 virtual sensor OTHER ROOMS METTI5 Spring School – T7 – S. Malan & C. Greco 9 METTI5 Spring School – T7 – S. Malan & C. Greco 10 Plant description Plant description Overall continuous time (CT) system definition Further inputs: • surrounding rooms temperatures → negligible effects T m (t) T r (t) State variable model: Plant Q(t) T a (t) • physical states: homogeneous bodies temperatures T e (t) (CT) • state number: model order Inputs: Outputs: • spatial discretization: great number of states • radiator input water • radiator output water • equations: heat exchanges equilibriums, physical temperature 𝑈 𝑛 temperature 𝑈 𝑠 parameters • heating water flow 𝑅 • room temperature 𝑈  𝑏 • external environment Simple models with few constraints temperature 𝑈 𝑓 Model order as a “black - box” identification parameter METTI5 Spring School – T7 – S. Malan & C. Greco 11 METTI5 Spring School – T7 – S. Malan & C. Greco 12 Models choice The continuous time (CT) dynamic system is represented by a discrete time (DT) model due to inputs and outputs sampling given by the technological configuration MODELS CHOICE T m (t) T r (t) PLANT Q(t) (CT) T a (t) SSV models T e (t) I/O models T m (i) T r (i) Q(i) ADC ADC T a (i) T e (i) ADC: number of bits 𝑂 sampling interval 𝑈 𝑡 sampling instant 𝑢 𝑗 = 𝑗𝑈 𝑡 , with 𝑗 the DT variable S. Malan & C. Greco - Politecnico di Torino 2

METTI5 Spring School – Tutorial 7 June 2011 METTI5 Spring School – T7 – S. Malan & C. Greco 13 METTI5 Spring School – T7 – S. Malan & C. Greco 14 Models choice Models choice: SSV models DT dynamic model representing the CT dynamic plant Time domain model     x ( i 1 ) Ax ( i ) Bu ( i )  T m (i) T r (i) Model    y ( i ) Cx ( i ) Du ( i ) Q(i) (DT)  T a (i)  given the initial condition x ( 0 ) T e (i) Z transform domain model Model characteristic:     zx ( z ) Ax ( z ) Bu ( z ) zx ( 0 ) • linear     • lumped parameters y ( z ) Cx ( z ) Du ( z ) Model classes: In stationary conditions, for an asymptotically stable • SSV : state space variable system, the initial condition is no more taken into account • I/O : input-output METTI5 Spring School – T7 – S. Malan & C. Greco 15 METTI5 Spring School – T7 – S. Malan & C. Greco 16 Models choice: I/O models Models choice: I/O models Z transform domain model Z transform domain model explicit form            y ( z ) N ( z ) N ( z ) N ( z ) u ( z ) N ( z ) y ( z ) G ( z ) u ( z ) y 0 z ( ) 1 1 1 , 1 , 2 1 , nu 1 01          y ( z ) N ( z ) N ( z ) N ( z ) u ( z ) N ( z )   1     1   2  2 , 1 2 , 2 2 , nu    02 2         The elements of 𝐻 𝑨 are transfer functions all having the        D ( z ) D ( z )   c     c   same denominator 𝐸 𝑑 𝑨 of degree 𝑜         y ( z )   N ( z ) N ( z ) N ( z )   u ( z )   N ( z )  ny ny , 1 ny , 2 ny , nu nu 0 ny The elements of 𝑧 0 𝑨 are rational proper functions all Consider a single input – single output model having the same denominator 𝐸 𝑑 𝑨 of degree 𝑜 N ( z )    jk y ( z ) G ( z ) u ( z ) u ( z ) In stationary conditions, for an asymptotically stable j jk k k D ( z ) c system, the initial condition is no more taken into account      n n 1  b z b z b z b   jk , n jk , n 1 jk 1 , jk , 0  u ( z ) y ( z ) G ( z ) u ( z )      n n 1 k  z a z a z a  n 1 1 0 METTI5 Spring School – T7 – S. Malan & C. Greco 17 METTI5 Spring School – T7 – S. Malan & C. Greco 18 Models choice: I/O models The derived difference equation is EXPERIMENTAL SETUP         ( ) ( 1 ) ( 2 )  ( ) y i a y i a y i a y i n   j n 1 j n 2 j 0 j AND DATA        b u ( i ) b u ( i 1 ) b u ( i n )  jk , n k jk , n 1 k jk , 0 k The model for a multi input – single output therefore is          y ( i ) a y ( i 1 ) a y ( i 2 ) a y ( i n )   1 2 0 j n j n j j         b u ( i ) b u ( i 1 ) b u ( i n )  j 1 , n 1 j 1 , n 1 1 j 1 , 0 1        b u ( i ) b u ( i 1 )  b u ( i n )  j 2 , n 2 j 2 , n 1 2 j 2 , 0 2         b u ( i ) b u ( i 1 ) b u ( i n )  j 3 , n 3 j 3 , n 1 3 j 3 , 0 3         b u ( i ) b u ( i 1 ) b u ( i n )  jn , n n jn , n 1 n jn , 0 n u u u u u u S. Malan & C. Greco - Politecnico di Torino 3