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Diskuse ke článku: Modelování a ovládání vnitřních teplot aplikací Matlab / Simulink pomocí modelu prostoru a přenosových funkcí

Autor článku: Ing. Mohamad Kheir Mohamad, Ph.D.
Plné znění článku: Modelování a ovládání vnitřních teplot aplikací Matlab / Simulink pomocí modelu prostoru a přenosových funkcí
Anotace článku: Tepelná bilance v libovolné zóně je základním principem pro modelování a simulaci vnitřní teploty. Stavový prostorový model zahrnuje celý matematický popis o dynamickém procesu, protože objasňuje stavové proměnné, vstupní signály a výstupní signály. Určením všech těchto parametrů je simulace řešitelná pomocí softwaru, kde lze provést validační proces.
Matlab / Simulink nabízí efektivní nástroje pro řešení stavově prostorového modelu a transformaci na jiné modely, jako je model na bázi přechodových funkcí. V Matlabu existují pokročilé nástroje, které analyzují systém a určují jeho reakce na různé typy vstupních signálů.
Cílem této práce bylo navrhnout stavově prostorový model pro simulaci vnitřní teploty v budově, zatímco vnitřní teplota a teploty ve vrstvách jsou stavovými proměnnými. Potom byl stavově prostorový model konvertován na přechodovou funkci pomocí control toolboxu v Matlabu. Systém byl poté analyzován pomocí nástroje ltiview. Tímto nástrojem lze určit základní charakteristiky jeho dynamických odezev. Poté byl navržen programovaný algoritmus pro návrh proporcionálního regulátoru v závislosti na přechodových funkcích získaných ze stavově prostorového modelu. Konečně byla pomocí Simulinku provedena simulace pro ověření výsledků.

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Re: Possible use cases of these models?MohamadKheir MOHAMAD29.08.2018 10:45
Possible use cases of these models?Jiří Cigler28.08.2018 22:07

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Předmět: Possible use cases of these models?
Autor: Jiří Cigler
Datum: 28.08.2018 22:07 odpovědět upozornit redakci

uživatel: 124835
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Hi,
Very interesting article for me, as a control engineer. I would have couple comments:
1) is the ultimate goal the design of a PID controller for steady state operation? Or what are your future plans with the model?
1.1) looking at step responses for varying P, it can be seen that the settling time is 25000s, which is 7hrs!! This is too much. Within 7 hrs, boundary conditions (outdoor temperature, internal gains, solar gains, etc.) can change. This change will certainly influence the controller performance. I believe that the response should be much faster.
2) typically, there is a maximum available power that can be delivered through the radiator. How does the linear theory go with the constraints on the maximal available power? If I count well, for control error of 2degC, the heat power output is 5kW, which can be for such a small room more than max power of installed heaters.
3) Having such a detailed model, I would certainly recommend the implementation of model predictive controller. The modelling is the most complicated part.

Předmět: Re: Possible use cases of these models?
Autor: MohamadKheir MOHAMAD
Datum: 29.08.2018 10:45 odpovědět upozornit redakci

uživatel: 128333
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Hi,
You are welcome. Thanks for comments and interaction with the article content.
Regarding first comment: as I have written in my article that “The model is designed to study the system performance and modify its construction if necessary before implementation. While simulation is the way to create a virtual time with virtual conditions, and investigate the system performance. Modelling and Simulation offers the ability to reduce the chances of failure and optimize performance for dynamic systems”
In this article, and by modelling, a residential room is heated with a P controller tuned by algorithm proposed in a way to overcome the influence of offset usually resulted from P controllers.
In control engineering, it is well known that PI performance is better than P performance, and PID performance is better than PI, and so on. But cost of temperature control with P controller is much lower than higher performances controllers, and more simple. It is usually (P controller) used where a precise control is not necessary, where the mass of the system is so great that temperatures change extremely slowly. So we have to balance between the performance and cost, so according to those points mentioned above, P controller is selected to control temperature. This modelling is a step to pave the way for other modelling using other control strategies, taking into account the cost.
Future work can be creating more real conditions, (multiple inputs) such as outdoor conditions, indoor gains or losses, heat capacity of indoor materials, and so on. In addition to investigate the influence of any modifications on the total cost. Hence, this model can be developed to take into account all those considerations.
The algorithm can be also developed to modify transient response of system (settling time, max overshoot, and so on).
Regarding settling time:(25000s) is sure big (note that settling time is for set temperature, not for minimum indoor temperature we want to obtain!!), but this is expected, because by looking at wall structure, it will be clear that there is no insulation material and thicknesses are small. Hence, the thermal resistances are so low. In such cases, thermal losses through walls are so high (and it is clear from heat balance equation, that solar radiations is neglected taking into account that process is heating. Internal gains are also neglected for simplification because occupancy in such small building is not high). The most important note is that control process in this article concentrates on (and only on) steady state value (minimum indoor temperature), not on the transient response. For that, heat calculated by algorithm is the minimum power to obtain that temperature. If we are interested in settling time we have to take into account more considerations, and we can rise (for example) power to allow heat to accumulate inside room, and as a result, settling time will be much lower. Regarding outdoor temperature: It is well known that to design HVAC systems, there is a design temperature outside ,which upon, heating and cooling loads are calculated. So, for any increasing or decreasing in temperature outdoor, controller must reset indoor conditions to meet the desired conditions. As a result form above considerations, it is clear that to increase temperature indoor from 0 to 20 in such case, a long time will be spent, taking into account the important influence of heat capacities of materials. Hence, heating becomes so expensive, or even useless, because heating load in some cases become much higher than actual power of HVAC systems. This is a big problem in Syria we are suffering from, and I am working on a research deals with it. I hope I publish parts of it as soon as I finish. Regarding your comment“ If I count well, for control error of 2 deg C, the heat power output is 5 Kw“: I do not think so!. Look carefully at table 2. It can give clear details.
Finally, Modelling is an art as well as a science, so each model can spot light on important point maybe is absent from other models.
There are a lot of control strategies. Fuzzy, Neural, Prediction, even coupled between many strategies. But again: balance between cost, performance and simplification must be carefully taken into account.

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