Cascaded control configurations

Practical considerations in implementing the hierarchical control framework developed above concern the availability of manipulated inputs to address the control objectives in the slow time scale (it is possible that dim(us) dim(ys)), as well as achieving a tighter coordination between the distributed and supervisory control layers. Both issues are effectively addressed by using a cascaded control configuration, which extends the choice of controlled variables in the slow time scale to include the setpoints y)p of the distributed controllers. 

In this case, however, the algebraic constraints in the DAE system describing the slow dynamics (3.22) will explicitly involve manipulated input variables (i.e., y p), and the direct application of the methods in Section 2.3 for the derivation of a state-space realization of the slow dynamics is not possible.2 

It can be shown (Kumar and Daoutidis 1996, Contou-Carrere el al. 2004) that, under some mild assumptions (including Assumption 3.1), the models of the process systems under consideration can be transformed into regular DAE systems by introducing an additional set of appropriately defined differential variables, i.e., by constructing a dynamic extension of the process model. Within this framework, considering that a subset y C ygp of the setpoints of the fast controllers are used as manipulated inputs in the slow time scale, the dynamic extension 

2 Differential algebraic equation systems whose algebraic equations explicitly involve manipulated input variables are referred to as nonregular (Kumar and Daoutidis 1999a). See also Definition A.6. 

Remark 3.4. In the context of the present chapter (and of the remainder of the book), the term hierarchical control structure reflects the use of two (or multiple) coordinated tiers of control action, and should not be confused with hierarchical plant-wide controller design strategies (see, e.g. Ponton and Laing 1993, Luyben et al. 1997, Zheng et al. 1999, Antelo et al. 2007, Scattolini 2009, and references therein), which use the term hierarchy to denote a set of guidelines, to be followed in sequence, for designing the control system for a chemical plant. 

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A potential choice of manipulated inputs to address the control objectives in the slow time scale is [ 3 Mrsp]t, i.e., the product flow rate from the column reboiler, and the setpoint for the reactor holdup used in the proportional feedback controller of Equation (3.35). This cascade control configuration is physically meaningful as well intuitively, the regulation of the product purity 23 is associated with the conversion and selectivity achieved by the reactor, which in turn are affected by the reactor residence time. 

The arguments presented above indicate that the large recycle and coolant flow rates wr and uq are the only manipulated inputs available in the fast time scale, and should be used to control the process temperatures. Likewise, the dynamics of the material-balance variables in the slow time scale are affected only by the small feed and effluent flow rates uq and up, which are thus the manipulated inputs that must be used to tackle control objectives involving the material balance. 6sp, the setpoints of the temperature controllers in the fast time scale, are also available as manipulated inputs in the slow time scale, a choice that leads to cascaded control configurations between the energy- and material-balance controllers. 

Since the flow rate of the feed stream Fo is fixed (and subject to disturbances arising from changes in the upstream process conditions), it is not available as a manipulated input in the slow time scale. Therefore, we address the control of the inventory and the product purity C b by employing, respectively, F and Tsp as manipulated inputs, the latter choice leading to a cascaded control configuration. 

Cascade control is one solution to this problem (see Fig. 8-35). Here the jacket temperature is measured, and an error signal is sent from this point to the coolant control valve this reduces coolant flow, maintaining the heat transfer rate to the reactor at a constant level and rejecting the disturbance. The cascade control configuration will also adjust the setting of the coolant control valve when an error occurs in reactor temperature. The cascade control scheme shown in Fig. 8-35 contains two controllers. The primary controller is the reactor temperature coolant temperature controller. It measures the reactor temperature, compares it to the set point, and computes an output, which is the set point for the coolant flow rate controller. This secondary controller compares the set point to the coolant temperature measurement and adjusts the valve. The principal advantage of cascade control is that the secondary measurement (jacket temperature) is located closer to a potential disturbance in order to improve the closed-loop response. 

The approach assumes that all the constrained variables can be measured or estimated on-line at a sampling period much smaller than the time constant of the controlled plant. Notice that the decision variables u in the RTO problem may very well be set points of feedback controllers acting directly on the plant manipulated variables. In this case, the constraint controller can be viewed as a primary controller in a cascade control configuration that corrects the set points produced at the RTO level. 

In Section 20.1 we assumed that the secondary process (process II, Figure 20.2a) in a cascade control system is faster than the primary process (process I, Figure 20.2a). Is this necessary to justify the use of a cascade control configuration In other words, would you still recommend cascade control for a process (like that of Figure 20.2a) with a secondary process much slower than the primary ... 

In a cascade control configuration we have one manipulated variable and more than one measurement. It is clear that with a single manipulation we can control only one output. Let us now examine the motivation behind cascade control and its typical characteristics using an example from the chemical processes. 

The plant-wide control system developed before is finally applied to the modelled process in HYSYS.PLANT and evaluated based on its close-loop dynamic behaviour and disturbance rejections performance. Once the control system of the non-heat integrated plant is validated, the favoured HEN design, based on its operational performance, is integrated within the entire plant and its control system is linked with the proposed plant-wide control structure mainly through cascade control configurations. 

For robustness purposes, let us regard a passive cascade control configuration (i) the tracked output (z) consists of measured (zn,) and unmeasured (zf) components (Eq. 2a), (ii) the output Zm must have relative degrees equal to one (RD s = 1) [9], with respect to the primary input (Up, xj), which consists of entries (up) of the input u, and of measured entries (Xs) of the state X (Eqs. 2a-b), (iii) the measured state Xs is regarded as the control input Uv (or the tracked output ys) of the primary (or secondary) control subsystem (Eq. 2c), and the secondary pair (Us, ys) has RD s = 1, and (iv) the state of the corresponding zero dynamics (ZD) [9] is referred to as xi (2d). These RD requirements determine the following control structure ... 

Figure 16.2 shows a cascade control configuration for the furnace, which consists of a primary control loop (utilizing TT and TC) and a secondary control... 

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