Identification of System Modelling and Predictive Control (Coursework Sample)

Module Code: EAC4001-N
Module name: Identification and Model Predictive Control
Assignment: In Course Assessment (I.C.A)
Student number: A0143510
Student name: Lewis Korir
Module leader: Prof. Michael Short
System Identification and Model Predictive Control.
Teesside University
(School of Computing, Engineering and Digital Technologies)
Module name: Identification and Model Predictive Control
Contents
TOC \o "1-3" \u \h List of Abbreviations. PAGEREF _Toc71222164 \h i
Abstract PAGEREF _Toc71222165 \h 1
Introduction. PAGEREF _Toc71222166 \h 1
Mathematical model PAGEREF _Toc71222167 \h 1
Designing a predictive controller. PAGEREF _Toc71222168 \h 3
Analysis PAGEREF _Toc71222170 \h 6
Conclusion PAGEREF _Toc71222171 \h 7
References PAGEREF _Toc71222172 \h 8
List of Abbreviations.
FOPDT- First Order Plus Dead Time.
IFOPDT- Integrating First Order Plus Dead Time.
SOPDT-Second Order Plus Dead Time.
ISOPDT- Integrating Second Order Plus Dead Time
Abstract
System modelling is the description of a system using mathematical concepts and terms. Control engineers examine the dynamics of a system and come up with a mathematical description of the dynamics. Modelling industrial processes directs one’s thinking to the concept of time delays. System delays can either be a true time delay or an apparent time delay. Apparent time delays arise due to high order dynamics. A plant made up of different real poles in cascade will exhibit time delay with the most prominent pole giving the main characteristics first-order exponential. Common process model structures include FOPDT, SOPDT, IFOPD and ISOPDT. The time delays incorporated into these models cover for pure and apparent delays. This paper will focus of mode parameter identification using reaction curve method and the design of a predictive controller for the modelled process. The process under closed loop predictive control should achieve se point tracking meaning that the controlled process variable eventually levels out without external intervention.
Introduction.
The reaction curve methods involve modelling of system parameters from the reaction curve itself. The transient response upon reaching as close to steady state as possible is used to find the gain (K), time constant (τ) and the delay time (d) for a FOPDT system. The FOPDT system model is expressed as.
Gs=Ke-sd1+ τ s Equation SEQ Equation \* ARABIC 1
K, d and τ vary with time and factors such as long-term operating conditions of the system.
The method is preferably used for an open loop transient response (no control action) where the process response can be isolated.
From the open loop transient response, the time taken for the response to reach 28.3% and 63.2% of the final steady state are noted. Say t1 and t2, respectively. For a first order lag, 28.3% and 63.2% response completion occur in τ/3 and τ time units respectively, we have: dead time+τ3=t28.3% and dead time+τ= t(63.2% ). From these two equations, the system parameters can be modelled as follows:
ddelay=1.5t1-t23 Equation SEQ Equation \* ARABIC 2
τ time constant=1.5 t2-t1 Equation SEQ Equation \* ARABIC 3
Kpgain=Kp=ΔyΔu Equation SEQ Equation \* ARABIC 4