The linearization method is applied to approximate the nonlinear system by using the linearized model [36, 39].
The experimental results are close to the results predicted by using the linearized model of the system and highlight many of the difficulties associated with the practical implementation of robust control laws.
The rheological parameters (surface tension and surface dilatational viscosity) for a number of contrast agents (Albunex®, Optison® and Quantison®) are determined by matching the linearized model dynamics with experimentally obtained attenuation data.
One possibility is to check for local observability or controllability of the reduced models by analyzing the linearized model equations (16) x → ˙ = A x → + B u → y → = C x → with A = (∂ f → (x →, u → ) ∂ x → ) x → o, u → o, B = (∂ f → (x →, u → ) ∂ u → ) x → o, u → o and x → ∈ ℝ n, u → ∈ ℝ m.
Controller performance has improved after the implementation of input shaping, with a reduction of the integral of the absolute error by 36% and of the settling time by 18%, despite the mismatch between the linearized model used by the input shaper and the actual non linear dynamics of the system.
end{aligned} Hence, if frac{2B T}{| mathbf{u}_{0} - tilde {mathbf{u}}_{0} |_{infty}} (21) is not very large, β is fairly large and, e.g., (alphageq 0.5), then the size of the error-amplification ratio (E(T beta)) is dominated by (I(T beta)), i.e. by the term stemming from the linearized model.
Secondly, dynamical effect caused by the uncertain parameters on the linearized model is analyzed, which reveals that the linearized model is affected by disturbance and affine parameter-dependent matrices.
Operating point stability analysis is performed by extracting the eigenvalues of the linearized model around the operating point at different solar irradiances.
The NGPC controller is designed based on instantaneous linearization model of the control system, and the parameters of the linearized model are identified online by the recursive least square method (RLSM).
Once the linearized model is provided by means of CREATE-NL code, the divertor coils currents are calculated using a constrained quadratic programming optimization procedure, in order to achieve HFE configuration.
