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Category: Control systems

Closed-loop weight control: the power of feedback

In this article, a closed-loop approach to human body weight control is presented. The main purpose of the article is to demonstrate that applying feedback has significant benefits over conventional open-loop techniques suggested in the rich health literature on the subject. In particular, a closed-loop approach is robust to the strongly adaptive mechanisms of the human body and to disturbances of various kinds. Also, in contrast to conventional approaches proposed in the health literature, the presented method based on feedback does not depend on any specific diet. In fact, the approach can be applied to any diet preferred by the subject.

DISCLAIMER: The proposed method has not been approved by medical doctors. If applied incorrectly, it can potentially cause significant health issues. It is strongly recommended not to pursue the experiments described below without consulting a physician.

Background

For a large and increasing proportion of the world population, overweight and obesity cause a wide range of health issues and in particular are leading causes of premature death. The World Health Organization (WHO) defines overweight as a Body Mass Index (BMI) greater than or equal to 25 kg/m2  and obesity as BMIs larger than 30 kg/m2. According to WHO, worldwide obesity has more than doubled since 1980. In 2014, almost two billion adults were overweight. More than 40 million children under the age of five were overweight or obese in 2014.

In part for health reasons, dieting has been recommended by medical doctors and other health experts for centuries, at least dating back to the early 18th century, e.g. by the English doctor George Cheyne, who based on personal experience recommended diets for anyone suffering from obesity or overweight as described in his 1724 report, An Essay of Health and Long Life. There is no shortage of descriptions of diets in contemporary literature, ranging from esteemed medical journals to popular magazines and newspapers. In Western societies, a significant proportion of the population has been following one or several such diets for longer or shorter periods of time. In addition to health challenges, overweight/obesity also have significant psycho-social effects.

In this article, we shall provide a control theory perspective on weight control. A simple feedback algorithm will be described below along with experimental data verifying the algorithm.

Modeling weight gain

The dynamics of human body weight is by far dominated by three factors:

  • Food and drink intake, instantaneously causing a (partly temporary) weight gain
  • Excretion, instantaneously causing a (partly temporary) weight loss
  • Metabolism, slowly but steadily causing (temporary) weight loss

Recent research has shown that exhaust from lungs (part of excretion) is a major factor in weight loss. Burning 10 kg human fat requires inhalation of 29 kg oxygen. This produces 28 kg carbon dioxide and 11 kg water. As food and drinks are temporarily stored in the human stomach and bowels, the body weight is instantaneously increased with the weight of any food or drink consumed. Metabolism is usually divided into catabolism and anabolism, where catabolism is the process of breaking down organic matter and anabolism is the reverse process of constructing proteins and nucleic acids. Metabolism is catalyzed by enzymes and metabolic rates can be strongly time and state dependent, governed by such catalyzing enzymes. In eukaryotes, such as homo sapiens, metabolism is connected to a series of proteins in mitochondria. As a very coarse model, the level of metabolism at any given time is therefore proportional to the number of mitochondria. The number of mitochondria depends strongly on tissue types and therefore on body distribution of these, but in the larger picture the number of mitochondria is positively correlated with the number of cells in the body, which is finally approximately proportional to the body weight. In summary, this rough reasoning leads to the following extremely simple model for body weight dynamics:

\[\frac{dw(t)}{dt} = -\alpha(w,t)\cdot w(t) – e(t) + f(t)\]

where \(w(\cdot)\)>0 is the body weight, α is a positive parameter, depending on state and time, that governs the metabolism,  \(f(\cdot)\) is the food/drink intake function, which can only attain non-negative values and \(e(\cdot)\) is the excretion function, which can only attain non-negative values. Clearly, this model cannot be expected to be accurate in open loop. E.g. it does not capture the difference in dynamics between catabolism and anabolism, which would require a higher order model. Below, however, we shall argue that this very simple model surprisingly suffices to understand and design closed-loop behavior.

Proposed control algorithm

The approach suggested in this article relies on the following assumptions:

  • Body weight is a measureable state variable
  • Food weight is a controllable input
  • Metabolic rates can be time-varying, but are bounded from below, α≥αmin

Based on these assumptions, a simple feedback control law that takes body weight as its measurement and specifies food intake as the control signal can be devised:

\[F(t) = r(t+T) – w(t)\]

where \[F(t) = \int_t^{t+T}f(\tau)\;d\tau\]is the weight of food and drinks consumed during a meal starting at time \(t\) and ending at time \(t+T\); further \[r(t+T)\] is the control reference at time \(t+T\) (the end of the meal). Since  \(f(\cdot)\) is a non-negative function, the reference \(r(\cdot)\) has to be chosen larger than \(w(\cdot)\) at all times.  In practice, the algorithm can rely on (suitably conservative) estimates for some meals, if an insufficient number of measurements are available, as long as the integral constraint is met during a day – please, see experimental data below.

A consequence of the above is that a reference with a weight loss demand larger than that dictated by the metabolism (catabolism) at any period of time, is infeasible. In practice, however, the reference weight loss should not only be marginally smaller but significantly smaller than the metabolic weight loss between two consecutive meals, as otherwise the body will not get a sufficient amount of nutrients for sustaining normal operation, and potentially health will be challenged. Further, when choosing a reference, it should be taken into account that α tends to be monotonically increasing/decreasing with a monotonically increasing/decreasing w, i.e. metabolism tends to adapt in order to changing weight (this is well-documented in the medical literature).

Experimental verification

The algorithm described above was applied during an experiment with a duration 44 days with the author of this article as the subject. A reference was chosen that had a constant slope for the first 31 days (one month), followed by a constant value. The initial value of the reference was chosen as the initial condition of the body weight. The final value of the reference was chosen as a body weight that would bring the BMI from an initial 26.1 kg/m2 (mild overweight) down to 23.8 kg/m2, i.e. well into the normal (non-overweight) area. In summary, this schedule inferred a weight loss of 7.4 kg during the 31-day weight loss period, i.e. a daily decrement of 239 g, followed by a static weight condition for 13 days.

 

Figure 1: Results of closed-loop weight control experiment

 

The experimental results can be seen in Figure 1. In practice, the algorithm was carried out by three daily body weight measurements: a morning measurement, a measurement immediately before the last meal of the day, and a late evening measurement for validation. The breakfast and the lunch meals were chosen to weigh approximately half the margin between the (known) upcoming evening reference and the morning measurement. That left about half the food intake for the evening meal, which was weighed on the plate and calibrated to match the remaining margin up to the scheduled reference. With this approach, the reference was normally reached by each evening measurement. Figure 1 shows a few overshoots. These happened at events where adhering to social code prohibited the meals from being weighed, so estimates had to be applied instead. Also, drinks taken after the last meal were not calibrated, which gave minor deviations. The undershoots in the beginning of the experiment are deliberate.

It is interesting to note that as the actual weight approaches the target, the metabolic cycles decrease significantly in amplitude. This is probably due to body responses that change the metabolic rates. It is likely that such a mechanism has developed evolutionarily to respond to periods of food scarcity. In contrast, metabolism is seen to increase significantly close to the end of the experiment, where the flat part of the reference has allowed a much higher food intake, causing the body to respond by what could perhaps resemble a food surplus scenario in an evolutionary context. Throughout the experiment, the conscious awareness of the subject provided another level of feedback, as the subject gained experience with the impact of his exercise, food composition, etc.

Conclusions

The closed-loop weight control approach proposed in this article has the virtue of offering deterministic results, based on the single assumption that the algorithm is followed strictly. It should be noted that the method is completely independent of any specific composition of the diet. In fact, although the daily weight loss of the experiment was significant, the involved diet throughout the experiment included a proportion of energy intensive food components such as chocolate and red wine (the red wine is discernible in the experimental results, causing the metabolic cycles to reduce significantly in two instances). Also, it should be noted that due to monotonicity properties of metabolic systems, any diet that has the same weight loss as in the described experiment, will have the exact same average food intake, provided the food has the same distribution of proteins/carbs/fats.

A limitation of the proposed approach is that it does not address nutritional adequacy aspects of diets. If one tries to lose weight too fast, or put a goal for a too-low ultimate steady state reference, one’s health will suffer. In practice the reference trajectory should be “reasonable.”

On the other hand, as an important conclusion of this article, feedback can be combined with any given diet, providing a layer of mathematically guaranteed weight loss to a physiology based diet that would typically be composed from a health perspective. The main approach to a healthy body will always be a healthy lifestyle with healthy food and lots of exercise. However, for anyone on a diet, there is simply no reason not to embed the diet in a closed-loop approach and take advantage of the power of feedback!

 

Article provided by:
Jakob Stoustrup
Department of Electronic Systems
Automation & Control
Aalborg University, Denmark
IFAC Technical Board

Control of Dynamical Systems by Partial Differential Equations

complex-bee-behaviour

Many phenomena are common to us all, but the way they work might be less well known. Why? They are dynamic systems! What is a dynamical system? Generally, it means that such kind of systems are described by Partial Differential Equations (PDE), and in order to study them, we have to understand their properties and we need to control some of them. We need to simulate the control developed in order to be sure that it fits exactly what it is expected, or to understand how a phenomenon is going on!

This intriguing area will be studied in a recently granted project “DYCON–Dynamic control”, which aims to develop a multifold research agenda in the broad area of Control of Partial Differential Equations (PDE) and their numerical approximation methods by addressing some key issues that are still poorly understood. To this end we aim to contribute with new key theoretical methods and results, and to develop the corresponding numerical tools and computational software.

The field of PDEs, together with numerical approximation and simulation methods and control theory, have evolved significantly in the last decades in a cross-fertilization process, to address the challenging demands of industrial and cross-disciplinary applications such as, for instance:

  • The management of natural resources (water e.g.),
  • Meteorology (make better weather predictions e.g., which involves big data problems and related numerical problems),
    aeronautics,
  • The oil industry (oil forage e.g., whose main problem is the friction at the bit),
    Biomedicine (cancer strategy via immunotherapy),
  • Human and animal collective behaviour, (understand behaviour of bees in order to anticipate their extinction, relations and interactions between several species) etc…

The ERC Advanced Grant DYCON project identifies and focuses on six key topics that play a central role in most of the processes arising in control applications, but which are still poorly understood: control of parameter dependent problems; long finite time horizon control; control under constraints; inverse design of time-irreversible models; memory models and hybrid PDE/ODE models, and the links between finite and infinite-dimensional dynamical systems.

These topics cannot be handled by superposing the state of the art in the various disciplines, due to the unexpected interactive phenomena that may emerge, for instance, in the fine numerical approximation of control problems. The coordinated and focused effort that we aim at developing is timely and much needed in order to solve these issues and bridge the gap from modelling to control, computer simulations and applications.

The ERC Advanced Grant DYCON provides resources to researchers willing to contribute to these endeavours within the research team led by Enrique Zuazua at Universidad Autónoma de Madrid-Spain.

Researchers interested in cooperation are welcome to get in contact with Enrique Zuazua (enrique.zuazua@uam.es, www.enzuazua.net).

There will be openings and opportunities for researchers in all career stages: internship PhD students from other centers and groups, PhD and postdoctoral contracts and one-quarter visiting positions of confirmed researchers.

 

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Word document  with references can be downloaded here (100KB)

Article provided by:
Valérie Dos Santos Martins
Laboratoire d’Automatique et de Génie des Procédés, 
Université Claude Bernard Lyone
TC 2.6. Distributed Parameter Systems

A survey on industry impact and challenges thereof

modern-society

At its 2014 World Congress, IFAC launched a “Pilot” Industry Committee with the objective of increasing industry participation in and impact from IFAC activities. I chair this committee with the support of Roger Goodall (Loughborough University, UK) and Serge Boverie (Continental, France) as co-chairs. This committee was established as an outcome of an Industry Task Force led by Roger Goodall in the last triennium.

In 2015 the committee undertook a survey of its members to get their views on the impact of advanced control and challenges associated with enhancing the impact. The survey had two questions. 23 of our 27 members then (excluding the chair) responded. The majority of the membership is either currently with or has prior affiliation with industry; all others have had substantial industry involvement as well. Most of the members were nominated by IFAC National Member Organizations and Technical Committees.

Although limited in many ways, I thought the survey responses would be of interest to the controls community.

Survey Question 1: Impact of Specific Advanced Control Technologies

First, we asked for members’ perceptions about the industry success (or lack thereof) of a dozen advanced control technologies. PID control was also included in the list for calibration purposes. A glossary was included with the survey, listing topics covered under each technology. Members were asked to assess the impact of each of these technologies by selecting one of the following:

  • High multi-industry impact: Substantial benefits in each of several industry sectors; adoption by many companies in different sectors; standard practice in industry
  • High single-industry impact: Substantial benefits in one industry sector; adoption by many companies in the sector; standard practice in the industry
  • Medium impact: Significant benefits in one or more industry sectors; adoption by one or two companies; not standard practice
  • Low impact: A few successful applications in one or more companies/industries
  • No impact: Not aware of any successful deployed real-world application

The results: The control technologies are listed below, in order of industry impact as perceived by the committee members:

Rank and Technology High-impact ratings Low- or no-impact ratings
1. PID control 100% 0%
2. Model-predictive control 78% 9%
3. System identification 61% 9%
4. Process data analytics  61%  17%
5. Soft sensing 52% 22%
6. Fault detection and identification 50% 18%
7. Decentralized and/or coordinated control 48% 30%
8. Intelligent control 35% 30%
9. Discrete-event systems 23% 32%
10. Nonlinear control 22% 35%
11. Adaptive control 17% 43%
12. Robust control 13% 43%
13. Hybrid dynamical systems 13% 43%


On the face of it, these results are disappointing. No advanced control technology is unanimously acknowledged by industry-aware control experts as having had high industry impact—90 years after its invention (or discovery), we still have nothing that compares with PID! It’s also concerning that the “crown jewels” of control theory appear at the bottom of the list.

However, the fact that all the technologies had at least some positive assessments suggests that the impact could well be higher than indicated: Many control scientists and engineers are likely not aware of the impact of control technologies outside the application domains of their experience. Thus the problem may be as much the perception as the reality.

Survey Question 2: Issues and Challenges with Industry Impact

The second question listed a number of statements and asked respondents to indicate their level of agreement with each. Agreement could be indicated as strongly agree, agree, neutral, disagree, or strongly disagree.

The statements and the levels of agreement are tabulated below. I have also noted any significant differences of opinion between the industry and academic members of the committee.

Statement Agreement Disagreement Academia/Industry
Industry lacks staff with the technical competency in advanced control that is required for high-impact applications 83% 4%
Control researchers are much poorer than researchers in other fields at communicating their ideas and results to industry management 26% 30%
The maturity or readiness level of results of advanced control research is too low for attracting industry interest 57% 22% 42% of industry respondents but no academic respondent disagreed
Advanced control has limited relevance to problems facing industries and their customers 4% 65%
The conflict between industry deadlines and academic research timelines is worse in control than in related engineering fields 30% 35%
Control researchers place too much emphasis on applied mathematics or advanced algorithms whereas successful industry applications require deep domain knowledge 83% 13%
Control researchers place too little emphasis on plant/process modeling and model-development methodologies 57% 17% No one from industry disagrees 30% of academics disagree
Students in control (undergraduate and graduate) are not sufficiently exposed to problems in industry 70% 13% No one from industry disagrees 30% of academics disagree
The academic control community is not seriously interested in collaboration with industry 26% 39% 33% of industry respondents but only 11% of academic respondents agree
There is no problem—advanced control is successful and appreciated in relevant industries 13% 83%

 

A clear message is that domain understanding/modeling is crucially important but not adequately pursued and taught. Neither expertise nor experience in advanced control per se is sufficient to realize industry impact.

Conclusions

This survey wasn’t, and nor was it intended to be, scientific or comprehensive, but I and my fellow committee members have found the results thought- and discussion-provoking. We are continuing to explore the challenging problem of industry impact from control research. Among other outputs, we expect to recommend specific enhancements to IFAC events, publications, and volunteer groups. Your feedback is welcome and will be appreciated!

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Word document  with references can be downloaded here (400KB)

Article provided by:
Tariq Samad
Senior Fellow
Honeywell/W.R. Sweatt Chair in Technology Management
The University of Minnesota
Vice chair, IFAC Technical Commitee

Consumer-driven automation for smartening the grid

NCPC_Power_Plant_Yellowknife_Northwest_Territories_Canada_08

Consumers are expected to play a considerable greater role in smart grid deployment and it is crucial to boost their awareness of this more active role. Smart grid is a great opportunity for all consumers, whose involvement in demand side management will significantly speed up the development of a smart grid market. The way the energy is used has to be revolutionised and, to actualize that, consumers need to understand what benefits they will achieve and how to change their behaviour to gain those benefits. All the players in the electricity system need to learn how to engage and effectively educate consumers, and improve their trust. We do not know the best way to make this happen yet, but we do know the highly negative impact of inadequate consumer engagement on future deployment plans. Thus, control solutions and automation systems for demand side management necessitate taking consumers into account, their preferences, their needs and uncertainty in their behaviour.

The next-generation electric grid needs to be smart and sustainable to deal with the explosive growth of global energy demand and achieve environmental goals. To effectively smarten the grid we need to rethink the roles and responsibilities of all players in the electricity system. This smartening is a progressive and revolutionary process (Figure 1). However different settings will be around the world and deployed at different rates, the use of information and communications technology to monitor and actively control generation and demand in near real-time is indisputably a common feature. Therefore, control and automation are essential for enabling consumers to actively support the grid.

Smarter-electricity-systems_blog
Figure 1. Smarter electricity systems (source: IEA, 2011) [Click on image to view larger version]

The increased control over the network can enable a wider, more sophisticated range of smart methods and innovative schemes, such as demand response and smart energy management systems for buildings, to facilitate local management of demand and generation. Demand response includes both manual and automated consumer response, smart appliances and thermostats, which are able to respond to price signals, or carbon-based signals. These smart devices are connected to an energy management system or controlled directly by the utility or a system operator. Smart energy management systems for buildings need to incorporate the user into the design and thus be responsive to their occupants in order to improve their comfort and allow smart appliances and heating systems to be on the market and respond to price signals to help decreasing the electricity bills. The benefits for consumers can be diverse, e.g., reduction of the electricity bill, improving of living conditions, supporting a more environmentally friendly energy behaviour.

In particular, smart energy management systems are required to be able to:

  • respond to signals from the grid and take action on this basis (e.g., decreasing energy use when prices are high or automatically shifting consumption to times when prices are lower);
  • manage local generation facilities, such as solar panels, and fed back into the grid any energy
  • optimally schedule storage devices, which can be used to balance out the smart grid.

Those advanced and innovative energy management systems make buildings smart and we can claim that a smart grid cannot exist without smart buildings. Hence, there will be more and more active roles for consumers of different sizes to play in a smart grid, for instance:

  • Residential consumers can choose among different tariff schemes and optimally shift smart appliance demand away from peak times through smart meters and energy management systems;
  • Industrial and commercial consumers can participate in the energy market through
    a wide range of demand response schemes;
  • Generator owners can participate in demand response schemes and the market by supplying needed energy to the grid.

Novel control and automation systems are becoming quite widespread, although standardised solutions are still not available, which means that expensive tailored configuration are required. This clearly limits the engagement of consumers, in particular small-scale consumers. In addition to designing and deploying control and communication solutions more affordable to a wider range of consumers’ sizes, effective motivational factors must be explored and thoroughly examined (e.g., environmental concerns, better comfort, control over electricity bills). The risk here is that consumers who do not make the savings expected from their behavioural change might consider the whole experience disappointing and frustrating.

Accurate, systematic and methodical research and evaluation are still needed to identify the optimal methodology to understand better the interaction between consumers and energy market, as well as the effect of enabling technologies for smart grid deployment.

A persistent behavioural change is vital to effectively enable smart energy technology development. We still need an answer to the following questions:

  • Is there an optimal mix of behavioural change, consumer feedback and automation technologies?
  • How much customer education is required and what are the best approaches?
  • Which types of automated demand response schemes are most useful to different types of customers (residential, commercial, industrial)?

Research groups, along with industry and governments, need to design and test more consumer-focused control solutions that can foster large-scale consumer behaviour change.

 


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Word document  with references can be downloaded here (400KB)

Article provided by:
Alessandra Parisio
School of Electrical and Electronic Engineering
The University of Manchestervice
IFAC Technical Committee 9.3 (Control for Smart Cities)

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