Stability is a key component of chemical process operability and represents the tolerance for small perturbations in the process, which is related to process benefits and safety. As one of the multiple steady-state solutions, the optimal operating point may be located in the unstable branch. 1, ...
The FIR structure has inherent properties such as a bounded input/bounded output (BIBO) stability and robustness against temporary modeling uncertainties and round-off errors. Filters require the unbiasedness as a basic requirement, that is, E[x̂k|k]=E[xk]. Since the initial state information...
yk. Unlike traditional regression models, this model does not contain all the prehistory, but rather especially selected vectors (the closest to the current input vector subject to a certain criterion) named “associations”. The least squares method provides a solution to this system of equations,...
The control input criterion function follows: 𝐽(𝑓𝑒(𝑘))=|𝑣∗(𝑘+1)−𝑣(𝑘+1)|2+𝜆|𝑓𝑒(𝑘)−𝑓𝑒(𝑘−1)|2J(fe(k))=|v*(k+1)−v(k+1)|2+λ|fe(k)−fe(k−1)|2 (9) Figure 2. Block diagram of the PPMLM direct thrust force ...
Since the load change and other nonlinear disturbances in practical applications have a great impact on the control effect of the system, an improved extended state observer is further used to compensate for the impact of nonlinear disturbances on the control system. In addition, the stability of ...
Utilizing the projection algorithm to estimate the PJM, therefore, the criterion function of this time-varying parameter is set as follows: 𝐽(𝛷(𝑘))=‖Δ𝑥̂(𝑘)−𝛷(𝑘)Δ𝑢(𝑘−1)−𝑓̂𝑑(𝑘−1)‖2+𝜇‖𝛷(𝑘)−𝛷̂(𝑘−1)‖2 (16) ...
4.3. Fatigue Fatigue is an important criterion for determining the structural integrity of materials printed by DED. The fatigue properties of AM parts have been studied by several groups [98–100] and recently reviewed by Bian et al. [101]. Fatigue is influenced significantly by the ...