The theory behind index funds is simple, of course, but achieving perfect tracking of the fund with its benchmark index is not.
The Dow Jones/UBS Commodity Index, for example, has shown a monthly correlation of 0.39, with 1.00 being a perfect tracking of the S.& P. index, said David Reilly, a chartered financial analyst and president of Decision Critical Resources in Boston.
Type-III control loops are capable of achieving perfect tracking of step, ramp and parabolic reference signals with zero steady state position, velocity and acceleration error.
In this way, both the perfect tracking of the current reference and disturbance rejection of grid voltage harmonic can be achieved.
The aim is controlling power converters in order to satisfy the following requirements: i) tight dc bus voltage regulations, ii) perfect tracking of SC current to its reference, and iii) asymptotic stability of the closed loop system.
Sufficient conditions are thus established that guarantee the closed-loop stability and the fact that both the actuator and the controller stop saturating after a finite transient period, implying perfect tracking of the output reference signal provided this is compatible with the actuator constraint.
The perfect tracking of references and the perfect robustness of controlled variables to perturbations are two aspects of integral control systems, i.e. the two features can be observed simultaneously for the same system.
We focused on the control structures leading to so-called 'perfect adaptation' , as defined by (i) complete robustness of the concentration of the pathway's end product towards perturbations in supply and demand, (ii) perfect tracking of perturbations by variables involved in the adaptation.
Phenotypic plasticity can allow a rapid adjustment to novel environmental conditions and even if this does not always allow a perfect tracking of the changing environment, as pointed out above, it could allow populations to persist in the short-term and 'buy time' for evolutionary adaptation in the long term (Chevin et al. 2010; Kovach-Orr and Fussmann 2013).
