(149i) Self-Optimizing Control for Secondary Controlled Variable Selection

The technique of self-optimizing control has garnered significant attention in recent times as a means of selecting controlled variables (Skogestad, 2000). This approach involves the conversion of the optimization objective of a process into a process control goal through the design of controlled variables, which can be a known function of measured variables with some tunable parameters. The self-optimized controlled variables are then maintained at a constant set-point to achieve optimal or near-optimal operation(Jäschke et al., 2017). Currently, the most commonly used method in SOC is to select a linear combination of measured variables as the controlled variable, that is, c=Hy, where c is the controlled variable, y is the measured variables, and H is the linear combination matrix.

Self-optimizing control finds a primary application in the design of control structures for continuous chemical processes, where controlled variables are selected with regard to the steady-state economic performance of the process(Jäschke et al., 2017). While a few studies consider dynamic factors, such as the work by Klemets et al.(Klemets and Hovd, 2019), who combined PI controller design with controlled variable design to achieve a trade-off between steady-state and dynamic performance, and research on the design of self-optimized controlled variables for batch processes are also emerged(Grema and Cao, 2020; Ye and Skogestad, 2018). Nevertheless, existing self-optimizing control methods concentrate on real-time optimization schemes that prioritize controlled variables design at the optimization layer. That means it focus to select the primary variable, and thus, the selection and design of controlled variables for regular control layers which is called secondary controlled variables remain unexplored. However, the proper selection of secondary measurements is a crucial challenge in the field of chemical process control, particularly in the case of multistage or distributed parameter systems that comprise key process units(Shen and Yu, 1990).

Typically, the primary variables are the variables we would really like to control, and secondary variables are the variables we control locally to make control of primary variables easier (Skogestad and Postlethwaite, 2005). As highlighted by Hsu et al. (1990), this control structure can be interpreted as an indirect feedforward control, given that the secondary controller acts as a feedforward controller for specific load changes. However, in practice, many process units experience multiple-load disturbances, leading to suboptimal parallel cascade control performance when the real load disturbance deviates from the nominal one used for secondary controller design. To address this issue, Shih-Haur Shen(Shen and Yu, 1990) proposes a measurement selection criterion to enhance disturbance-rejection averaging. However, these methods are rarely applicable to nonlinear systems. Secondary variables selection based on a linear model is the easiest and most efficient. However, it may be ineffective, since the nonlinear plant may loose desirable properties due to linearization, like controllability.(van de Wal and de Jager, 2001)

The same issue exists in the early research of SOC. Early efforts to address the SOC CVs design problem focused on linear analysis for the sake of simplification(Alstad et al., 2009; Alstad and Skogestad, 2007; Halvorsen et al., 2003; Kariwala, 2007; Kariwala et al., 2008). The localness of self-optimizing performance remains a significant challenge for the local linear analysis, particularly when the chemical plant is significantly nonlinear and operated under drifting points. The method known as global SOC (gSOC) approach(Ye et al., 2015) minimizes the average loss when disturbances are distributed across the entire uncertain space. This method starts from the optimal data and no longer depends on the local linear model when designing the controlled variable.

Moreover, the secondary variables selected by these studies were single measurements. Nevertheless, limited by current sensor technology, it is difficult to achieve optimal rejection of each disturbance based on a single measurement.

Minasidis et al.(Minasidis et al., 2015) proposed that in the design of plant-level control structures, the secondary controlled variable can also be represented by a linear combination of measured variables within the control structure of the conventional control layer. However, the authors refrained from undertaking a comprehensive evaluation of the advantages and consequences of utilizing such an approach.

This paper considers extending the global self-optimizing control to the structure design of the regular control layer to introduce a nonlinear design method of system output design, and expanding the secondary variables for a single measurement to the linear combination of the measured variables, so as to improve the resistance of a process to disturbance.

In this paper, we use the averaging integrated error defined by Shen(Shen and Yu, 1990) to identify the effects of disturbances on primary loop variable outputs in the presence of secondary loops.

The proposed method is applied to an industrial-scale superheated steam drying process for shredded tobacco. In this process, the tobacco is continuously conveyed via a feed-in vibratory conveyor and an infeed airlock into the acceleration bend, where the tobacco is dried by heated process gas (hot air) flow with a temperature of approximate 150-300 ℃. After a very short drying time (total retention time of the tobacco in the dryer is about ten seconds), the tobacco is ejected from the superheated steam dryer via a cyclone with a discharge airlock. Part of the process gas is vented and the residual circulated via a process gas fan to the process gas heater where it is heated up. Then the ejected cut tobacco is conveyed along the vibratory conveyor into the winnower where it gets thoroughly mixed and eventually moves to the next process.

According to product quality requirements, it is expected that the moisture content of cut tobacco before moves to the next process will remain constant at the set value. So the primary goal of this process is that the final cooled moisture is constantly maintained at the desired level. However, this process has two dynamic modes with extremely different time constants, fast and slow, making it difficult to control the cooled moisture stably constant. In this paper, the global self-optimizing control method is used to design secondary variables to have better rejection ability to various disturbances. The method has been tested in both the mechanism model and the actual plant. The selected secondary control loop significantly reduces variations in the cooled moisture, hence verifies the concept that self-optimizing control can also be applicable to secondary controlled variable design.

The contribution of this paper lies :

1. The global self-optimizing control method is expanded to the structure design of the regular control layer. And it is successfully applied to the superheated steam drying process for shredded tobacco.
2. By introducing a nonlinear design method of system output design and expanding the secondary variables for a single measurement to the linear combination of the measured variables, which can improve the resistance of the process to disturbance.

Overall, the proposed method offers a promising solution for controlling the moisture content of cut tobacco in a superheated steam drying process, which is challenging due to the multiple dynamic modes with extremely different time constants. By designing a set of better secondary variables that are resistant to disturbances, this method can help improve product quality and increase process efficiency.

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