326285 An Approach to Total State Control in Batch Processes Through Distributed Control Structures

Monday, November 4, 2013: 2:10 PM
Continental 8 (Hilton)
H. Marcela Moscoso-Vasquez, Gloria Milena Monsalve-Bravo and Hernán Alvarez, Universidad Nacional de Colombia, Medellín, Colombia

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.

A description...

Fig 1. SII for the state variables of the penicillin reactor: biomass concentration (x1), product concentration (x2), substrate concentration (x3) and reactive mass' volume (x4).

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.

Table 1. Input -- Output pairings for the process.

MaD: x3

MaD: x1

Pairing

x1 -- u1

x2 -- u2

x3 -- u1

x2 -- u2

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.

A description...

Fig 2. State profiles obtained by the proposed TSC approach.

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Fig 3. State profiles optimized by Banga [9].

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.


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