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Written in a clear, logical and concise manner, this comprehensive resource provides discussion on essential mathematical tools, required for upgraded system performance. Understanding of basic principles and governing laws is essential to reduce complexity of the system, and this guide offers detailed discussion on analytical and numerical techniques to solve mathematical model equations. Important concepts including nonlinear algebraic equations, initial value ordinary differential equations (ODEs) and boundary value ODEs are discussed in detail. The concepts of optimization methods and sensitivity analysis, which are important from subject point of view, are explained with suitable examples. Numerous problems and MATLAB®/Scilab exercises are interspersed throughout the text. Several case studies involving full details of simulation are offered for better understanding. The accompanying website will host additional MATLAB®/Scilab problems, model question papers, simulation exercises, tutorials and projects. This book will be useful for students of chemical engineering, mechanical engineering, instrumentation engineering and mathematics.
Using a single symmetric relay feedback test, a method is proposed to identify all the three parameters of a first order plus time delay (FOPTD) model. On identifying a higher order dynamics system by an FOPTD model, the conventional method identifies a negative time constant (Li et al., 1991) due to the error in neglecting higher order dynamics in the system output. In the present work, all the parameters of an FOPTD model are estimated with adequate accuracy. Four simulation examples are given. The estimated model parameters of an FOPTD model are compared with those obtained by Li et al. (1991) and also those with the exact model parameters of the system. The performance of the controller designed on the identified model is compared with that identified by Li et al. (1991) and with that of the actual process. The method gives results close to that of the actual system. Simulation results for stable and unstable systems are given.
Identification of transfer function models from experimental data is essential for model based controller design. Often derivation of a rigorous mathematical model is difficult due to the complex nature of chemical processes. Hence, system identification is a valuable tool to identify low order models, based on the input-output data. The relay feedback is a single-shot experiment and the magnitude of oscillations can be varied. From the principal harmonics approximation, the ultimate gain (Ku) and ultimate frequency (ωu) are found.