(662f) Feedforward Control with Block-Oriented Modeling with Demonstration to Nonlinear Parametrized Wiener Modeling

            This work proposes a feedforward
control (FFC) approach with block-oriented modeling. It is demonstrated using a
nonlinear parametrized Wiener Modeling approach in feedback feedforward (FBFF) control.
The process used for this demonstration is a simulated continuous stirred tank
reactor (CSTR) with four (4) measured inputs. The Wiener model is nonlinear in
the physically-based dynamic parameters of the transfer functions and linear in
the static parameters of the static gain function. The static gain function has
a second order linear regression form with interaction and quadratic
terms.  The Wiener model is built under
open-loop conditions using a Box-Behnken
statistical experimental design consisting of 27 sequential step tests. Under a
sequence of multiple input changes, the addition of feedforward control (FFC) reduced
the standard deviation of the controlled variable from its set point by 70%.  

Traditional
feedback control (FBC) makes adjustments to some manipulated variable after the
process has deviated from its desired operating condition or set point (SP) for
the controlled variable. In the past few decades, more sophisticated control
algorithms have been introduced that use models determined from process data to
achieve tighter control. Some of the most well-known model-based control
systems include FFC, internal model control (IMC), and model predictive control
(MPC).  However, while FFC is the only model-based
control system that can totally cancel the effect of a disturbance,
theoretically, it appears to have seen limited implementation in real processes
as indicated by the very low number of articles in the process control
literature. For effective FFC the model must consists of only inputs and the
inputs have to map accurately and causatively to changes in the controlled
variable which is very difficult to achieve in modeling real data for several
reasons. The first one is due to shifts in the output caused by changes in the
levels of unmeasured disturbances. Minimizing the number of unmeasured
disturbances by measuring them and including them in the set of inputs can help
to alleviate this behavior but as the number of inputs in the model increases,
the complexity of the model increases and parameter estimation becomes more
difficult. Furthermore, as the number of inputs increase, the longer the data
collection will need to be and thus, the greater the likelihood of shifts in
the output from changes in unmeasured inputs. Secondly, causative input
modeling accuracy will suffer when the inputs are pairwise cross-correlated, especially
for structures with linear parametrization. Finally, over the input operating
space, the inputs typically map nonlinearly to the response space due to
interactive and curvilinear relationships between the inputs and the output. As
a consequence of these modeling challenges, FFC in practice has often been
limited to a few variables, narrow input ranges, and linear static gain functionality.

Some models for
nonlinear gain behavior have been proposed for model-based controllers
including radial basis functions (RBF),
genetic algorithms (GA), Nonlinear Auto
Regressive Models And eXogenous
inputs (NARMAX) models, and block-oriented models
(BOMs). An important advantage of NARMAX and BOMs is that they can use transfer
functions, i.e., linear dynamic equations with physically interpretable
parameters. However, a limitation of the NARMAX structure is that all of its
transfer functions have the same characteristic equation or denominator
dynamics. BOMs use the outputs from blocks of dynamic (transfer) functions that
are linear (L) differential equations as inputs to functions that can be
nonlinear (N) with respect to static gain parameters. The simplest of the BOMs
is the Hammerstein network (NL), which has an N block followed by an L block
and the Wiener network (LN), which reverses the order of these two blocks. More
complicated block-oriented structures include sandwich models such as an LNL
network, which has linear dynamic blocks, followed by a nonlinear static block,
followed by a second linear dynamic block. When the inputs can have different
dynamic behavior, the Wiener network is the preferred choice over Hammerstein
and is superior to NARMAX because the inputs can have completely different
dynamic structures.

A number of
researchers have studied the identification of model parameters for the
Hammerstein and Wiener networks. The LNL network has not gotten as much
attention, but some have proposed methods for its parameter identification. There
has been much progress over the last decade in the identification of BOMs and recently,
by taking a nonlinear parametrized approach for estimation of the dynamic
parameters, accurate Wiener modeling was demonstrated using nine (9) inputs on
a real distillation process with large variation due to unmeasured disturbances
and with highly pairwise cross-correlation of the inputs. While there has been
progress in the use of BOMs in model based control, progress of FFC using BOMs
appears to have been limited to single input models. Thus, the objective of
this work is the development of a general FFC framework for multiple-input BOMs
in FFC with nonlinear static gain behavior. This framework will be demonstrated
using a nonlinear parametrized Wiener modelwith a second-order static gain
structure on a simulated CSTR. The Wiener model is built under open-loop
conditions using a Box-Behnken statistical
experimental design consisting of 27 runs or sequential step tests. Under a
sequence of multiple input changes, the addition of feedforward control reduced
the standard deviation of the controlled variable from its set point by nearly 70%.