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The three Taylor expansion derivatives are constructed in one large image using the completed set of basis filter responses.
This paper discusses the control of an ideal reactive distillation column (RDC) using model predictive control (MPC) based on a combination of deterministic generalized orthonormal basis filter (GOBF) and stochastic autoregressive moving average (ARMA) models.
In the polar transform, we use the same interval to discretize angular and roll angles, and thus, the basis filter w t can be defined as begin{array}rcl@ {{boldsymbol{w}}_{boldsymbol{t}}} = left[{w_{{boldsymbol{t}},{theta_{1}}}},{w_{{boldsymbol{t}},{theta_{1}}}}, cdots,{w_{{boldsymbol{t}},{theta_{nz}}}}right] end{array} (19).
To make the scalable basis filter reflection-shiftable [29], we further design C j (r)(j = 0, 1) as: C j r = a j cos π 2 log 2 2 r π + R j + a j cos − π 2 log 2 2 r π + R j = 2 a j cos R j cos π 2 log 2 2 r π. (13).
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The radial component of the SPT's basis filters was taken as the kernel for designing the scalable basis filters.
The radial component of the SPT's basis filters is taken as the kernel of the scalable basis filters, and the angular component is used for the steerable basis filters.
These were further combined with the steerable basis filters corresponding to the angular components of the SPT's basis filters, resulting in joint scalability and steerability.
Hence, the gradient can be estimated using steerable Gaussian first derivative basis filters: (12) (13).
To design such a filter, we explore the feasibility of capturing system dynamics using generalized orthonormal basis filters (GOBF).
For the convenience of construction, we uniformly adopt J = 2 scalable basis filters for all three cases.
According to the theory of shiftability in [29], scalable basis filters are essentially scaled versions of B k (r, θ).
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