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6). Due to the non-linearity, in this case there are three equilibrium points. 4]T ∂fi The Jacobian elements, aij = ∂x (xs , us ), of the linearised model can be easily j computed. , if needed. Matlab : Some commands implementing algorithms related to the contents of this section are: gradient,diff,ss. 5. A linearised model can also be obtained around a nominal trajectory. If the system input is defined in a time interval, u0 (t), ∀t ∈ [ti , tf ], and the nominal state trajectory is given by x0 (t), a linearised model can be attached to this nominal trajectory by relating the variations of the trajectory with respect to variations of the nominal input.
Thus, their level of detail, range of validity and presentation will be determined by their use. For each application, control goal or design methodology, a given model will be more or less suitable. Given a process, different models can be attached to it, some of them being equivalent, but, in any case, all them should be “coherent” [84]. For instance, for regulatory and tracking purposes, a CT/DT dynamic model would be required, but for production optimisation or management a simplified and aggregated model, or even a steady-state model, would be more appropriate.
However, with a proportional regulator, k = 85, the first system exhibits a wonderful, desirable, closed-loop step transient but the second one is unstable. 8) the second one is unstable in open-loop response. However, the behaviour with the above mentioned proportional regulator yields a very similar response in terms of settling time and final value. Thus, in modelling a process, the control purpose should be kept in mind. Identification for control is the identification approach trying to get the best process model to design the control and, moreover, to combine the efforts of modelling and control design in the common endeavour of getting the “best” controlled system behaviour.
