Challenges arising from the model mismatch issue can be overcome through the use of estimation techniques simultaneously with the mp-MPC design, as discussed in Naşcu et al. The nonlinearity compensation is only implemented for the nominal patient and not for the exact values of each patient therefore, this approximation introduces an error in the control design. This strategy aims at controlling the drug concentration C ˆ e using a linear controller and is used in the next section of the design of the explicit/multiparametric controller. Here the inverse of the Hill curve is implemented in the controller with the nominal patient model parameters in Nascu et al. 11 based on a parameter scheduling technique shown in Nascu et al. Piecewise linearization leading to a piecewise affine formulation ( Dua et al., 2002 Oberdieck and Pistikopoulos, 2015). Local linearization (described in Naşcu et al., 2015). In general, the nonlinear part of the model corresponding to the Hill curve can be addressed as follows: In low-birefringence fibers, typically B m is less than 10 - 6, and the beat length exceeds 1 m. The beat length is defined as L B = λ / B m and it can be as small as 1 cm in high-birefringence fibers with B m ∼ 10 - 4.
When low-power, continuous-wave (CW) light is launched with its polarization direction oriented at an angle with respect to the slow axis, the polarization state of the CW light changes along the fiber from linear to elliptic, and then back to linear, in a periodic manner (see Figure 1.9 ) over a distance known as the beat length. Assuming n x > n y, n x, and n y are the mode indices along the slow and fast axes, respectively. These axes are called the slow and fast axes based on the speed at which light polarized along them travels inside the fiber. Agrawal, in Nonlinear Fiber Optics (Fifth Edition), 2013 6.1.1 Origin of Nonlinear BirefringenceĪ fiber with constant modal birefringence has two principal axes along which the fiber is capable of maintaining the state of linear polarization of the incident light.