Dynamic modelling of a control valve
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Process industries today enjoy significant benefits from advances made in the field of simulation as well as technologies that model normal plant operation. Plants however continue to suffer during abnormal operation such as start-up, shutdown and equipment failures leading to production losses or personal injury. One of the key elements that determines the operational safety of any plant is the training and technical knowledge of its personnel regarding plant behaviour. Simulators play a vital role in training personnel, preparing them for normal plant operation, abnormal plant operation as well as emergency and accident situations. This would not only enhance plant safety, but also decrease total downtime. In order to create such a simulator, mathematical models are required for each of the numerous components within the plant. This dissertation focuses on the development of a mathematical model for a control valve; a component commonly found in various industries to control and manipulate processes. Different modelling methods are compared, taking into account applicable modelling criteria such as training data, algorithm complexity, oscillations near endpoints, degree of system integration and model limitations. Based on these criteria, fuzzy logic with the nearest neighbourhood clustering algorithm is chosen as an appropriate modelling technique especially due to its ability to deal with large quantities of data. In order to meaningfully train the fuzzy logic system (FLS), a comprehensive set of physical operational data is required, covering all the different operational characteristics. To capture physical data, the development of a data acquisition (DAQ) system is introduced using two common DAQ systems to create a hybrid solution. Transducer signals are converted tom mA to V, using custom developed signal conversion hardware. This will allow data to be sampled by a standard DAQ card and processed by accompanying software. Two post- processing software applications are created. The first application solves the governing equations (mass rate of flow, Reynolds number, expansibility factor and choke status) and the second application is used to graphically display the acquired and calculated data. A set of experiments are conducted, covering all relevant working areas, to capture the behaviour of the control valve. This is achieved using five initial pressures ranging from 200 kPa to 400 kPa in increments of 50 kPa. At each initial pressure a set of unit step responses with valve command signals ranging from 0 % to 100 % in increments of 5 % is acquired. 24 data files at each initial pressure set (200, 250, 300, 350 and 400 kPa) are acquired. Before training the FLS, the optimal fuzzy logic parameters need to be determined e.g. radius (r), sigma (σ)the number of time delays, the time delay increments and the impact of the input signals. Determining these parameters is an iterative process. Only a single data set, with initial pressure of 300 kPa, is used to derive the optimal fuzzy logic parameters. Four performance criteria namely maximum error average (MEA), mean square error (MSE), root mean square error (RMSE) and coefficient of variation of the error residuals (CVRE) are used as benchmarks to obtain the optimal fuzzy parameters. During both the search for the optimal fuzzy parameters and the training of the fuzzy models using these optimal fuzzy parameters, 70 % of the data are used for training and verification while the remaining 30 % of the data are used for validation. Once the optimal fuzzy parameters are obtained using only the single data set, it is used to derive a number of fuzzy control valve models based on all the available data sets. All derived fuzzy models use the same parameters, except for a unique random file sequence associated with each of the models. The only prerequisite for the fuzzy models is that the generated file sequence be truly random. Irrespective of the random file sequence, fuzzy models with the same parameters, produce models with more or less the same performance. Therefore the performance criteria (MEA, MSE, RMSE and CVRE), for each data file, in the respective initial pressure sets, remains more or less the same. This method is found to be very useful in deriving a dynamic fuzzy logic control valve model. Averaging the performance criteria of these five models, an overall modelling accuracy of 90 % is achieved. It is recommended that a flow meter be installed to measure the mass rate of flow through the pipe network. This eliminates the need for an orifice, differential pressure transducer and the use of the first principle governing equation for the mass rate of flow. If a flow meter cannot be installed, a differential pressure transmitter with large range should be considered accompanied by a single orifice.
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