(137f) An Approach to Total State Control in Batch Processes Through Distributed Control Structures

AN APPROACH TO TOTAL
STATE CONTROL IN BATCH PROCESSES THROUGH A DISTRIBUTED CONTROL STRUCTURE

In Batch Processes (BP)
raw materials are loaded in predefined amounts and they are
transformed through a specific sequence of activities (known as
recipe) by a given period. In this way, a determinate amount of a
specific product is obtained after a given time [1] . This sort of
operation is very important in specialty chemicals industry [2], and
it also represents the natural way to scale-up processes from the
laboratory to the industrial plant [3].

In order to address
control strategies for BP, it is important to distinguish between
discontinuous (including batch and semi-batch processes) and
Continuous Processes (CP). The two main differences between these
kinds of processes are: (i)
Time-varying characteristics in BP and (ii)
the end-product quality (run-end output) is the real control
objective in BP [2]. However, the main characteristics of batch and
semi-batch processes which imply a challenge for process control
engineers are: (a)
dynamic operating point, (b)
irreversible behavior, (c)
nonlinear behavior and (d)
constrained operation.

However, the literature
presents many particular cases (nothing generalizable) and the
studies on this topic have been limited to proposing a control
strategy and evaluating its performance in simulation, as can be seen
from [1],
[2], [4], [5].
Additionally,
there are no tools to evaluate properties as controllability and
stability in BP highlighting the lack of tools for designing control
strategies for this kind of processes.

It is frequently found
in BP that not enough control loops are installed over the process.
Only those measurable variables are controlled regardless if those
variables can or cannot be associated with product quality. This fact
places BP control under a critical situation regarding the required
end-product quality given the irreversible character of these
processes, because of which, any deviation for the desired operation
gives a different end-product quality [1].

As a way to overcome
these issues, a new approach for Total State Control (TSC) in BP
based on the dynamics hierarchy of the process and a distributed
control structure is proposed. The dynamics hierarchy allows the
classification of process variables in (i) Main Dynamic (MaD)
constituted by one dynamic behavior that relates both process
characteristics and process objective and (ii) Secondary Dynamics
(SeD). Since TSC follows the line of controlling all states in a
process, in this work the proposed approach has the explicit
requirement of controlling all SeD in a way that MaD and therefore
product quality are driven to pre-established values during batch
operation.

The process' dynamics
hierarchy is determined by an extension of the discrete control tool
called Hankel matrix which has been widely used in model reduction,
systems identification, digital filter design, and recently in
controllers design for establishing input -- output pairings in
continuous processes [6]. This tool uses a Phenomenological-Based
Semiphysical Model (PBSM) for representing the process and Hankel
matrix for: (i)
representing the dynamic behavior of the process in input -- state
terms, (ii)
determining the effect of all the input variables over each state
variable, constituted by the State Impactability Index (SII) of each
state variable; (iii)

Determining the effect of each input variable over all state
variables, constituted by the Input Impactability Index (III); and
(iv) establishing the states and inputs hierarchies to create control
loops, and selecting as MaD the state variable with the highest SII.

The SII and III are
computed by means of Singular Value Decomposition (SVD) of the Hankel
matrix. However, since Hankel matrix is a tool used in linear
processes and linearization of BP is not possible given the
inexistence of a unique process operating point; an extension for
using this tool in BP is developed considering a piecewise
linearization of the process.

Given the sequential
nature of BP that can be seen as transformation stages the product
undergoes, each stage can be considered as independent process
equipment so then the single BP is analogue to a process plant
composed by this individual process equipment with high energy and
mass interactions. As such, BP can be controlled using plant-wide
control strategies. The control strategy here proposed involves a
collaborative integration of the SeDs controllers to guarantee the
behavior of the MaD through single control loops for each SeDs, which
allows reaching a TSC for BP. This corresponds to a distributed
control structure, but based on coordination on PID controllers for
regulatory level with model-based coordination for optimizing
reactor's operation [7] instead of the usual MPC controllers [8], in
order to guarantee the performance of the control system while
maintaining a simple structure for its implementation.

The control structure
consists of two control layers: (i)
regulatory layer which deals with the SeDs control, and (ii)
supervisory layer which defines the set points for the regulatory
controllers. These set points are obtained by minimizing the
deviation on the MaD over the batch time using as manipulated
variables the set points for the SeDs controllers.

Finally, the proposed
approach is applied to a fed-batch penicillin reactor, using as
reference trajectories for MaD the optimal trajectories found by
Banga [9]. The dynamics hierarchy of the process is presented in Fig.
1, where is worth noticing that it changes during the batch run,
being x₃
(substrate concentration) the MaD during the first 20 h and after
that x₁
(biomass concentration) becomes the MaD. This means that at batch's
starting point the substrate concentration is the dominant dynamic
since it regulates biomass growth (inhibited at high substrate
concentrations) and therefore penicillin production. Then, when the
biomass has grown, its concentration becomes the dominant dynamic
since it regulates penicillin production and substrate consumption.

Then, pairings on the
regulatory level where determined computing the SII for the states
corresponding to SeD, except for x₄
(reactive mass' volume) since it can be considered constant during
the batch run. The available control actions are the substrate's
input flow (u₁)
and concentration (u₂).
For this, the state variables with the higest SII is paired with the
input variable with the highest III [6]. On Table 1, the pairing of
variables for each stage of the batch considering the change on the
MaD is presented.

A comparison between the
state profiles obtained by the proposed approach (Fig. 2) and
optimized by Banga [9] (Fig 3) shows that a higher penicillin
production can be achieved by means of the proposed TSC approach.

The main contribution of
this work is the usage of an index to determine a dynamics hierarchy
and using it for establishing control objectives and controlling all
the states of the process by coordination of SeD to achieve the
regulation of MaD, instead of only controlling only one variable
during the batch. Additionally, the design of the control loops is
made considering the controllability and observability of the process
(SII and III), and therefore its dynamic characteristics, instead of
stationary tools (as RGA) for an inherently transient process.
Finally, the proposed approach represents a paradigm shift in terms
of reconfiguration of the control system so it can respond to the
changes on the dynamic characteristics of the process as it evolves
in time.

REFERENCES

[1] L.
M. Gomez, "An approximation to batch processes control (in
Spanish)," Universidad de San Juan, Argentina, 2009.

[2] D.
Bonvin, B. Srinivasan, and D. Hunkeler, "Control and optimization
of batch processes," Control
Systems, IEEE,
vol. 26, no. 6, pp. 34--45, 2006.

[3] D.
Bonvin, "Optimal Operation of Batch Reactors - A Personal View,"
Journal
of Process Control,
vol. 8, no. 5--6, pp. 355--368, Oct. 1998.

[4] C.
A. Gomez, "Model Predictive Control (MPC) whit guaranteed stability
for batch processes (in Spanish)," Universidad Nacional de
Colombia., Medellin, Colombia, 2010.

[5] B.
Srinivasan and D. Bonvin, "Controllability and Stability of
Repetitive Batch Processes," Journal
of Process Control,
vol. 17, no. 3, pp. 285--295, 2007.

[6] L.
A. A. Toro and J. J. Espinosa, "Methodology based on SVD for
control structure design (in Spanish)," XIII
Congreso Latinoamericano de Control Automatico,
p. 6, 2008.

[7] V.
R. Radhakrishnan, "Model based supervisory control of a ball mill
grinding circuit," Journal
of Process Control,
vol. 9, no. 3, pp. 195--211, 1999.

[8] B.
T. Stewart, A. N. Venkat, J. B. Rawlings, S. J. Wright, and G.
Pannocchia, "Cooperative distributed model predictive control,"
Systems
& Control Letters,
vol. 59, no. 8, pp. 460--469, 2010.

[9] J.
R. Banga, E. Balsa-Canto, C. G. Moles, and A. A. Alonso, "Dynamic
optimization of bioprocesses: Efficient and robust numerical
strategies," Journal
of Biotechnology,
vol. 117, no. 4, pp. 407--419, Jun. 2005.