lunduniversity.lu.se

# FRTN35 - System Identification

## Systemidentifiering, 7.5 hp

 Syllabus Course program 2019 CEQ

## PLEASE NOTE: This course is replaced by FRTN65 Modeling and Learning from Data from 2021

System Identification (7.5 credits, 70 h): This advanced/doctoral course gives theoretical and practical knowledge of methods to develop mathematical models from experimental data. Transient response analysis. Frequency response analysis. Spectrum analysis. Linear regression. Times series models. Interactive identification. Mathematical modeling. The experimental procedure. Model validation. Model approximation. Real-time identification. Continuous-time models. Multidimensional systems. Nonlinear system identification. Subspace model identification.

### News

• (8/11) The exam correction is completed and the results have been posted to Ladok. Please contact exam responsible Tommi Nylander if you want to view your exam.
• (30/10) The solution to the exam has been posted under Previous exams.
• (04/10) Sign-up is now open for Lab 3.
• (04/10) Problem 1 in Homework 3 is revised.
• (19/9) Sign-up is now open for Lab 2.
• (6/9) Sign-up is now open for Lab 1.
• (3/9) The 2019 edition of the course starts on Tuesday Sep 3 at 13.15 in M:E. Welcome!

### Projects

Project Outlines

The project seminar will take place in the lecture hall Seminar Room M:2112B on Friday, Dec 6 at 10.15am.

### Other material

Solutions Manual to System Modeling and Identification

Home work assignments due by Sunday, September 15; September 29, and October 6

Other course material (Local access only)

Identification Data for Exercise Session 7

## Master Thesis Proposals

### Active Control of a Turbulent Jet

General motivation:

Turbulent flows and turbulent flow related problems are relevant to many devices that are necessary for our everyday-life comfort (e.g. cars, airplanes, ventilation systems …). Although the history of fluid mechanics research is rather long, turbulence remains a difficult problem since it is inherently non-linear and requires a 4D description. Recent progresses in flow simulations provide a better knowledge of turbulent flows and bring the hope of being able to control and optimize flow fields for improving existing systems.

Description of thesis work:

The main goal of the present work is to use numerical tools for simulating and controlling a turbulent jet. The jet will be described using Large Eddy Simulation (LES). The student will use the LES data for deriving control procedures in order to improve the mixing between the jet and its surrounding. For example, the student will study the efficiency of the control procedure by trying different configurations of sensor/actuators.

Suitable Student background:

Good knowledge of general fluid mechanics or control theory.

References:

T. R. Bewley, Flow Control: New Challenges for a New Renaissance, Progress in Aerospace Science, Vol. 37, 2001, pp. 21-58.

Contact information:

Christophe Duwig, Division of Fluid Mechanics (M-huset, 2nd floor North, room 2138)

Email: Christophe.Duwig@energy.lth.se - Tel: 046 222 31 84

Rolf Johansson, Dept Automatic Control (M-huset, 5th floor South)

Email: Rolf.Johansson@control.lth.se - Tel: 046 222 87 91

Figure 1: Vorticity field in a 2D jet from Yuan et al. (IEE Proc., 2004) a) unforced jet, b) & c) close-loop controlled jet, d) open-loop forcing.

As opposed to traditional approaches to adaptive control based on dynamic feedback and local gradient search, subspace-model identifcation is a block-data method that require substantial reorganization of  the adaptive control algorithms. Such algorithmic reorganization including analysis of properties constitutes this thesis assignment.

Methods: Theoretical analysis and simulation

Prerequisites: FRT041, FRTN15

Contact: Prof Rolf Johansson (Rolf.Johansson@control.lth.se)

Subspace-model Identification in Iterative Learning Control (ILC)

As opposed to traditional approaches to adaptive control based on dynamic feedback and local gradient search, subspace-model identifcation is a block-data method that require substantial reorganization of the adaptive control algorithms. However, this property fits the problem formulation of iterative learning control. The task of this thesis is to exploit the block-data nature of subspace-model identification to the benefit of iterative learning control. Apart from algorithm organization, this thesis topic includes analysis of  the resulting ILC properties with respect to stability, convergence and finite-time performance.

Methods: Theoretical analysis and simulation

Prerequisites: FRT041, FRTN15

Contact: Prof Rolf Johansson (Rolf.Johansson@control.lth.se)

Experimental Study of Adaptation and Postural Control after Sleep Deprivation

Background:
Human balance control is a complex feedback control system, which uses information from multiple different movement receptors and senses that interacts to enable a robust balance control. Sensory input from the vestibular and the visual organs combined with input from multiple proprioceptive receptors is reviewed, interpreted and processed by the postural control system. The balance control is usually highly effective and very precise even though it is normally managed without conscious control.  However, a certain mental alertness might be needed when the balance control have to adapt to new unknown constraints and to balance control perturbations that may require a new movement pattern behavior. Decreased mental alertness is usually associated with medication, but may also be evoked by alcohol intoxication or due to sleep deprivation.
Goal: The objective is to study whether reduced mental alertness due to sleep deprivation,affects the human balance control and the ability to adapt the movement pattern when the balance control is disturbed by pseudorandomized perturbations.
Methodology: 12-14 normal subject is investigated with posturography after 24 hours and 36 hours of sleep deprivation, and a control posturography trial is performed either 1 week before or 1 week after the sleep deprivation trials. The test subjects stand on a force platform, which measures the torques and shear forces induced towards the ground by the subjects to maintain balance, and the movement of the body segments are measured by a 3D ultrasonic positioning system. The posturography trial consists of two test, one test where the subjects are instructed to look at a reference point and second test where the subjects are instructed to stand with eyes closed. The body sway is initially measured for 30 seconds of unperturbed stance followed by 205 of perturbed stance where body movements are evoked by vibrators placed on the calf muscles. Quantitative analysis methods and system identification methods should be used to assess whether the subjects sway pattern and ability to adapt to a balance perturbations are changed due to sleep deprivation.

Contact information: Prof Rolf Johansson <Rolf.Johansson@control.lth.se>; Per-Anders Fransson, Senior Research Engineer, Balance Laboratory,  <Per-Anders.Fransson@onh.lu.se;

Experimental Study of Alcohol intoxication and Alcohol metabolization in humans.

Background: Alcohol has been used as a drug for many thousand years. Alcohol has various effects on the human body and influences the body functions from cellular level as well as the whole organism in both acute intoxication and in long lasting alcoholism.
However, there are only approximate models regarding the likely alcohol intoxication level a certain alcohol volume may produce in an individual human. These models are primarily based upon body weight and gender factors. A recently performed study has showed that these approximate models are rather inaccurate, particularly for heavier subjects. Some findings also suggest that the alcohol metabolization rate may be non-linear and individually different. Moreover, in human’s regular ethanol intake can induce tolerance and dependence. Thus, the maximum alcohol intoxication level and metabolization rate might be different in subjects, which more frequently drink alcohol.
Goal: The objectives of this study is to develop better models describing the likely maximum alcohol intoxication level to a certain alcohol volume and describe the likely metabolization rate over time.
Methodology: Data have been gathered from a test group of 27 subjects drinking an individual selected alcohol volume intended to give a maximum blood alcohol level of either 0.6 ‰ or 1.0 ‰.  The blood alcohol level was monitored by a breath analyzer within 15-30 minutes intervals for a period of 3-5 hours.
<>The individual information about the subjects consists of alcohol intake, age, gender, height, weight, body mass index (BMI), lean body weight, drinking habits scoring and subjectively sensed alcohol intoxication level during the trials.  A combination of the individual subject information, based on relevance for the measured alcohol intoxication levels, might be used do develop more accurate models describing the likely maximum alcohol intoxication level and metabolization rate over time on group basis.

Contact information: Prof Rolf Johansson <Rolf.Johansson@control.lth.se>; Per-Anders Fransson, Senior Research Engineer, Balance Laboratory,  <Per-Anders.Fransson@onh.lu.se>

Experimental Study of Adaptation of Postural Control and after-effects to Postural Control Adaptation.

Background: Adaptation and habituation are common in many biological systems and effects of adaptation in the human biological system can for example be observed in the motor control and in the central nervous system. If a repeated disturbance of the balance control is intense enough, an adaptive process is usually initiated to improve the control performance. A recently performed study has shown that the immediate adaptive response to balance perturbations are increased correlation between the body segment movements, which suggests that the subjects alter their kinematics and adopt a more rigid posture with coordinated motions of all body segments. In terms of motion control, a more rigid body posture has several advantages. A co-contraction of the antagonistic muscle groups increases the stiffness of a joint and increases the damping of the induced motions. However, a rigid posture and increased muscle co-contraction substantially increase the local and global energy cost used to maintain mechanical stability, which also increase the risk for fatigue in the muscles that requires high metabolic energy consumption to maintain the current state.

Goal: To investigate whether adaptation to a balance control task may induce post-effects that negatively affect the balance control even after the balance perturbations have subsided.

Methodology: 12-14 normal subjects are investigated twice with posturography; one initial trial and a second trial after 30 minutes to observe post-effects.
The test subjects stand on a force platform, which measures the torques and shear forces induced towards the ground by the subjects to maintain balance, and the movement of the body segments are measured by a 3D ultrasonic positioning system.  The posturography trial consists of two test, one test where the subjects are instructed to look at a reference point and second test where the subjects are instructed to stand with eyes closed. The body sway is initially measured for 30 seconds of unperturbed stance followed by 205 of perturbed stance where body movements are evoked by vibrators placed on the calf muscles. After the perturbation phase the body sway is measured during unperturbed stance for an additional time of 120 seconds. Quantitative analysis methods and system identification methods should be used to assess whether the subjects sway pattern and the ability to adapt to repeated posturography trials are changed due to negative balance control post-effects.

Contact information: Prof Rolf Johansson <Rolf.Johansson@control.lth.se>; Per-Anders Fransson, Senior Research Engineer, Balance Laboratory,  <Per-Anders.Fransson@onh.lu.se>

Modeling water vapor sorption hysteresis and scanning

Background: The interaction of water with solid materials like pharmaceuticals, textiles, dried food stuffs, building materials and paper is a technically very important process. Many material properties, including strength, durability and transport properties, depend on the water content of materials. The most common way to quantify materials-water vapor interaction is by sorption isotherms, the moisture content as a function of the surrounding relative humidity. For many materials this relationship is complex as there is a pronounced sorption hysteresis, i.e., there is one curve for desorption and one for absorption (at the same relative humidity a material holds more water when it is drying than when it is taking up humidity). When the external relative humidity fluctuates (as it often does in practice) the moisture content will be a complex function of the relative humidity history. For cement based materials the sorption hysteresis is very pronounced and this has some practical consequences. For example will a drying flooring material that is slightly moistened by the water in a water based flooring adhesive increase its relative humidity (water activity) significantly, which may lead to high rate of degradation of the polymer based adhesive.

Goal: To make a model of sorption hysteresis and scanning based on experimental data on a cement based material.

Methology: At Building Materials we have advanced sorption balances that can be programmed to expose a sample to steps and ramps of relative humidity, while the moisture content of the sample is measured by weighing. Firstly we will use such an instrument to measure limiting absorption and desorption isotherms and a set of scanning curves. Secondly, the acquired data will be used to propose a model of the moisture content as a function of the relative humidity history. We will limit ourselves to one material.

Contact information: Prof Rolf Johansson rolf.johansson@control.lth.se; Doc Lars Wadsö and PhD student Anders Anderberg at Building Materials lars.wadso@byggtek.lth.se.

Application of system identification methods on a complex experimental device to study energetics of biological systems

Background: A simple black box model of the metabolism of living systems (mammals, fungi, insects, bacteria etc.) contains one input (oxygen) and two outputs (carbon dioxide and heat). We have at Building Materials developed an instrument to measure these three parameters while the oxygen level decreases form atmospheric levels to low values. We have used the instrument to study mold fungi and potato tissue, the latter in collaboration with Food Engineering. During a measurement four parameters (thermal powers and pressures) are measured at two chambers in the instrument (a sample and carbon dioxide absorbent), between which oxygen, carbon dioxide and nitrogen can diffuse. To be able to evaluate the wanted parameters a valve between the two chambers closes and opens at regular intervals. The output from and experiment is dynamic and it has not been possible to make but a simplified evaluation of the response of the biological system to changes in oxygen and carbon dioxide pressures.

Goal: To apply system identification methods on the results from the method with the aim of extracting more information about the biological system.

Methology: To understand the experimental method a simple biological system is chosen, for example a mold fungi, and some measurements are made. Then an analysis of possibilities to improve the evaluation method with system analysis tools is made, and these are applied on the measurements.

Contact information: Prof Rolf Johansson rolf.johansson@control.lth.se; Doc Lars Wadsö, Building Materials lars.wadso@byggtek.lth.se.

Modeling the activity of biological systems as functions of temperature and humidity history

Background: All biological organisms need water to live, but some organisms such as mold fungi (“mögel”), lichens (“lavar”) and mites (“kvalster”) can by different mechanisms survive quite low humidities and thereby cause us problems: mold growth on food stuffs and building materials, allergic reactions from house dust mites that live in our beds etc. At Building Materials we have developed efficient methods to study the activity (respiration) of these organisms at different temperature and relative humidity conditions. The aim of our work is to be able to build models of the activity/growth of these organisms as functions of temperature and relative humidity, but this is complicated by the probable history dependence of these processes. For example, consider a fungi that we have measured the activity of at optimal 20oC/80% RH and at not at all optimal 40oC/80% RH and found that it is much higher at the first conditions. If we expose the fungi to the first conditions 23 h and the second severer conditions for 1 h on a daily basis, we may find that the activity/growth is very low. The reason is that the second set of conditions damages the fungi and the 23 h at optimal conditions cannot be utilized because it takes more than 23 h to recover from the 1 h high temperature exposure.

Goal: To propose a model that can be used to model the activity of one organism as a function of temperature and relative humidity.

Methology: To analyze possible forms of relations between temperature and relative humidity for one organism, set up models and test them on data measured at Building Materials.

Contact information: Prof Rolf Johansson rolf.johansson@control.lth.se; Doc Lars Wadsö and PhD students Yujing Li and Sanne Johansson at Building Materials lars.wadso@byggtek.lth.se;.

Optimization of a double thermostat for an isothermal nano-calorimeter

Background: Isothermal calorimeters are used to measure the thermal power produced by physical, chemical and biological processes. Most such instruments are placed in water thermostats that are both quite expensive and need frequent maintenance. We have developed a new extremely sensitive nano-calorimeter that is placed in a Dewar (vacuum) flask instead of in a liquid thermostat. This design works well and is used, e.g., at Building Materials to study the degradation of wood at 60-120oC. The temperature of the calorimeter is controlled by two serially connected thermostats, that we believe can be further optimized to gain lower noise and increased sensitivity.

Goal: To optimize the control of the two thermostats to achieve low noise under different external conditions.

Methology: Firstly the calorimeter design will have to be understood and critical parameters measured (for example the heat loss from the Dewar). Then a model of the calorimeter will be built, different control algorithms tested and implemented on a test instrument.

Contact information: Prof Rolf Johansson rolf.johansson@control.lth.se; Doc Lars Wadsö at Building Materials lars.wadso@byggtek.lth.se;.

# Example: Robot Data

Control input (chirp variation of motor voltage) and resulting position of two segments of a robot arm as observed from experiment (solid line; arbitrary units). The estimated position of the same robot segment positions are shown (dashed line; almost indistinguishable from data) when responding to the same input sequence as that of experimental data. Notice the resonance towards the end of the data recording.

Rolf.Johansson@control.lth.se