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In many applications, PSA is used to generate parameter ranking based on the magnitude of sensitivity coefficients, either taken at a specific time or using consolidated sensitivity metrics, such as time-integral or average or norm of sensitivity coefficients [ 34, 43, 44].
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The disturbance model is fixed in the controller, based on the internal model principle, and the other controller parameters are computed by convex optimization to meet the constraints on the infinity-norm of sensitivity functions.
For an interval system, we prove that the maximal H∞ norm of its sensitivity function is achieved at twelve (out of sixteen) Kharitonov vertices.
According to Yao et al. [ 25], the most identifiable parameter is the one with the highest Euclidian norm of the sensitivity vector, that is, max j ‖ b θ j ‖.
These are the infinity-norm of the sensitivity and complementary sensitivity functions and the crossover frequency.
Coefficient sensitivity functions of transfer functions with respect to filter additive/multiplicative coefficient variations are defined, and the H∞ norms of the sensitivity functions are used to measure the sensitivity of the transfer functions with respect to additive filter coefficient variations.
The process synthesis and design are carried out simultaneously with the MPC tuning to obtain the most economical plant which satisfies the controllability indices that measure the control performance (H∞ and 11 norms of different sensitivity functions of the system).
It is shown that performance specifications given as the infinity norm of the weighted sensitivity functions can be represented as convex constraints in the Nyquist diagram.
For this purpose, the matrix gains of controller are calculated such that the closed-loop system be stable, and simultaneously, the infinity norm of the weighted sensitivity function is minimized.
The method uses different design parameters: The infinity norm of the complementary sensitivity function as well as the crossover frequency are considered to represent the closed-loop system performances.
Then, this solution is substituted in the BRL to arrive at an LMI whose solution determines the gains of a stabilizing MIMO PI/PD controller which also minimizes the infinity norm of the weighted sensitivity function.
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