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Nonlinear Identification&Control with Solar Energy Applicate

wellsee / 2011-09-27
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Keywords: Solar inverter | voltage inverter | charger inverter | sine wave inverter | off-grid inverter | solar controller | MPPT | solar panel | charge controller | solar regulator


Canton Fair (first phase)

Date: from October 15 2011-Oct 19, 2011.

Code: 250EE330

Booth number is 5.1G40.

Place:China Foreign Trade Centre (382, Yuejiang Zhong Road, Guangzhou 510335, China )




mobil: 0086-13423949641


Nonlinear systems occur in industrial processes, economical systems, biotechnology and in many other areas. The thesis treats methods for system identification and control of such nonlinear systems, and applies the proposed methods to a solar heating/cooling plant.
Two applications, an anaerobic digestion process and a domestic solar heating system are first used to illustrate properties of an existing nonlinear recursive prediction error identification algorithm. In both cases, the accuracy of the obtained nonlinear black-box models is comparable to the results of application specific grey-box models. Next a convergence analysis is performed, where conditions for convergence are formulated. The results, together with the examples, indicate the need of a method for providing initial parameters for the nonlinear prediction error algorithm. Such a method is then suggested and shown to increase the usefulness of the prediction error algorithm, significantly decreasing the risk for convergence to suboptimal minimum points.
Next, the thesis treats model based control of systems with input signal dependent time delays. The approach taken is to develop a controller for systems with constant time delays, and embed it by input signal dependent resampling; the resampling acting as an interface between the system and the controller.
Finally a solar collector field for combined cooling and heating of office buildings is used to illustrate the system identification and control strategies discussed earlier in the thesis, the control objective being to control the solar collector output temperature. The system has nonlinear dynamic behavior and large flow dependent time delays. The simulated evaluation using measured disturbances confirm that the controller works as intended. A significant reduction of the impact of variations in solar radiation on the collector outlet temperature is achieved, though the limited control range of the system itself prevents full exploitation of the proposed feedforward control. The methods and results contribute to a better utilization of solar power.

User Comment

Anonymous user: give point ( 2011-10-22 11:33:02 )
2.1.3 Modeling Approaches
Discrete and Continuous Time Models
Apart from choosing a model structure a decision needs to be made about whether the nonlinear model of the system should be formulated in discrete or continuous time. For discrete time systems the choice may be easy, but data from continuous time systems is usually collected through sampling, which means that the data is discrete. There is consequently a choice between a model which describes a discretized version of the system at certain sampling instances, and a model that describes the continuous time system. One obvious advantage of the use of a discrete time model is that it seems intuitive to fit discrete time data to a discrete time model. In addition, many of the methods

28 2. Technical Starting Point
for system identification developed during the last three or four decades have been focused on discrete time modeling, so there are numerous tools to choose from. Other advantages include that it is easy to handle noise and time delays. Continuous time models, on the other hand, provide a description of the continuous time system, which is particularly useful in controller design, as most nonlinear control theory is based on a continuous time description of the system. For grey-box models, which are common in continuous time modeling applications, there is the additional advantage of having physical interpretations of the parameters. Conversion of a discrete time model to continuous time can be complicated, particularly for nonlinear systems. If the sampling has generated non-minimum phase zeros, it may even be impossible, at least for the linear case [6]. The sampling and reconversion to continuous time may in itself introduce errors in the discrete time model. On the other hand, generating a continuous time model from sampled data will in many cases require calculation of numerical approximations of derivatives. For the derivative approximations to be accurate the sampling rate is required to be high, which in turn makes the the derivative approximation sensitive to noise. For discrete time linear systems the Z-transform, and the corresponding shift operator
Anonymous user: give point ( 2011-10-22 11:27:51 )
2. Technical Starting Point
ODE models that are discussed in this thesis fit directly into the framework of the control methods described in e.g.
Both linear and nonlinear identification methods can be described as being either of black-box or grey-box type. In a grey-box, or semi-physical method, the modeling is performed using a priori knowledge of the physical properties of the system. Unlike grey-box models, a black-box, or non-physical, model is a mathematical description of a system, where little or no consideration is taken to the physical connection between different system variables. This implies that there may not be a complete physical interpretation of each part of the black-box model, which may under certain circumstances be considered a drawback. Clearly, little a priori knowledge of the system is required, and since the model is not tailored to the application, one model structure can be used for numerous applications, cf. e.g. for a further discussion.
The problem of modeling nonlinear dynamical systems has not been as extensively covered as the modeling of linear systems. The main reason for this is that an introduction of nonlinearities greatly complicates the modeling procedure.
For example, one linear model could be used to locally describe a large number of nonlinear systems. Consequently, if a linear model is not general enough to describe a particular nonlinear system there are several types of nonlinear models to choose from when determining a nonlinear model structure.
2.1.1 Grey-box Identification
A grey-box, or semi-physical, model is based on known relations of the system, and utilizes physical properties in e.g. mechanical processes, chemical reactions, or electrical circuits. The identification is focused on estimation of unknown parameters of the models, cf. The main advantage of this type of method is that available knowledge of the system dynamics is utilized
in the modeling and optimization procedures. However, the use of first principles makes each model application specific and can therefore not be used for identification of a different type of system. This is particularly true in the nonlinear case. It also presupposes that the model structure derived from first principles is sufficiently complex to describe the system in question. There is also a risk of making the physical model too detailed, leading to an overly complex model structure and estimation of more parameters than necessary. In such cases model reduction may be of interest.
2.1.2 Black-box Identification
In cases when prior knowledge is limited or grey-box modeling for other reasons is difficult to perform, there are still a number of black-box approaches described in the literature that can be applied. This section gives an overview of nonlinear black-box identification methods. It should be noted that the methods mentioned here do not constitute a complete list but are merely examples of the wide range of methods for system identification that can be categorized as nonlinear and of black-box type.
Block Oriented Methods
Another way of interpreting the Wiener model (2.3) is as block dynamics. The Wiener model can then be seen as a cascaded system consisting of a multiple input-multiple output (MIMO) linear dynamic system to which a static nonlinearity is applied at the output. The above observation is the reason why systems with the block structure of Fig. 2.1a are denoted Wiener systems. This block structure has a counterpart in the Hammerstein model where the static nonlinearity acts directly on the input signal and the linear block acts on the transformed input (see Fig. 2.1b). Though visibly similar, it is significantly easier to identify the linear dynamics in the Hammerstein model than in the Wiener model. The reason is that the Hammerstein model can be transformed to a linear multiple input-single output (MISO) model by a suitable choice of parameterization. A wide variety of methods have been developed based on the structures of Fig. 2.1, and related block structures. See e.g [84; 89] and the references therein for detailed algorithms and analyses.
Anonymous user: give point ( 2011-10-22 11:21:41 )
Another motivation for the study of nonlinear systems is the use of model based nonlinear control. A large variety of systematic design methods based on nonlinear ordinary differential equation (ODE) models have emerged in the last two or three decades. Feedback linearization and backstepping are two examples of the more important methods. To design controllers like
these a nonlinear ordinary differential equation model of the system is usually required. Consequently, tools from the system identification field for producing such models become highly interesting. The methods for identifying nonlinear
Anonymous user: give point ( 2011-10-22 11:20:03 )
Technical Starting Point
2.1 Nonlinear System Identification
System identification concerns mathematical modeling of dynamic systems based on measured data. The use of measured data makes the method inherently experimental, and the objective is normally to obtain a model that describes the behavior of the original system sufficiently well for the model to serve its purpose. Such purposes can be anything from an increased understanding of the underlying dynamics of the system to simulations, tracking of dynamics, fault detection, and controller design. The generality of system identification makes it applicable in industrial processes and biotechnology, as well as chemistry and economy, just to mention a few examples.

Many systems have nonlinear dynamics, which complicates the modeling.
Some examples of applications where nonlinearities occur include pH control, control valves, flight dynamics, and power systems. In certain cases a linear model may be sufficient to describe the system, at least around some operating point. However, it is e.g. shown in that linear models may be sensitive even to small nonlinearities, in which cases standard validation tools may not give a correct image of how well the model actually describes the system. In other cases, e.g. flight dynamics, the behavior of the system varies so much over the allowed operating range that gain-scheduling or adaptive control schemes are required. For such systems it may be advantageous to use nonlinear models with a wider operating range.
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