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**Extra info for Control Engineering Solutions: A Practical Approach**

**Example text**

4 Figure 2,9 Field of isoclines with marked inclinations, switching lines Ln L2 and trajectory x(t) If the non-linear element, such as a clipper or multi-level element, is step-wise linear, then the trajectories can be constructed by switching the solutions of the different linear fields. 9). Simulation is a useful method of checking the results. 10). Control structures of different complexity can be built, as the different components are linked by wires according to a given block diagram. The programmable signal generator produces the necessary inputs for control and distortion.

Subsequently, analysis of the algorithm residuals will be carried out to decide on the disturbance structure. 13 will be considered. e. the loss function — is computed over a data set for each of the runs. The structure giving the least value of the loss function, while maintaining simplicity, is chosen. It should be taken into account that if a model structure is evaluated on the same data set on which it was estimated, the loss function will always decrease as the model structure orders (na and nb) are increased (whereas this is not true for the delay d).

4 X(K)O l(XKK) 12OOO KKKM) 12OOO KMKK) 12(KX) 1(K)O() 12OOO Offset removal for Tsand qw Model structure selection A correct model structure has to be determined for each of the process loops to be identified. e. the correct orders for polynomials A and B and the correct delay d. A set of tests are available for evaluating these points [4,7,12], including: Determination of A and B orders Delay, d Perturbations structure Test Loss Function Determinants ratio Residuals variance decrease Loss function Poles-zeroes cancellation Residuals analysis Let us consider the pilot plant pHs/qb and Ts/qw loops and apply two of the most widely used tests for the determination of the polynomial order; the loss function and the residuals variance decrease methods.