Disturbances variable

One such approach is called cascade control, which is routinely used in most modern computer control systems. Consider a chemical reactor, where reac tor temperature is to be controlled by coolant flow to the jacket of the reac tor (Fig. 8-34). The reac tor temperature can be influenced by changes in disturbance variables such as feed rate or feed temperature a feedback controller could be employed to compensate for such disturbances by adjusting a valve on me coolant flow to the reac tor jacket. However, suppose an increase occurs in the... 

Sodium valproate Inhibits GABA 600-1200 mg/day Neurologic disturbances, Variable efficacy seen in Cushing s... 

There are other system inputs that can affect our closed-loop response, and we consider them load (or disturbance) variables. In this case, the load variable is the inlet temperature, Tj. Now you may understand why we denote the two transfer functions as Gp and GL. The important point is that input means different things for the process and the closed-loop system. 

Example 1.5. For a binary distillation column (see Fig. 1.6), load disturbance variables might include feed flow rate and feed composition. Reflux, steam, cooling water, distillate, and bottoms flow rates might be the manipulated variables. Controlled variables might be distillate product composition, bottoms product composition, column pressure, base liquid level, and reflux drum liquid level. The uncontrolled variables would include the compositions and temperatures on aU the trays. Note that one physical stream may be considered to contain many variables ... 

Thus the transfer function of a feedforward controller is a relationship between a manipulated variable and a disturbance variable (usually a load change). 

In the development of a general state-space representation of the reactor, all possible control and expected disturbance variables need to be identified. In the following analysis, we will treat the control and disturbance variables identically to develop a model of the form... 

Input variables are controllable, uncontrollable and disturbance variables. Controllable variables or factors X1 X2,..., X are variables, that can be directed or that can affect the research subject in order to change the response. They can be numerical (example temperature) or categorical (example raw material supplier). Uncontrollable variables Z1 Z2,..., Zp are measured and controlled during the experiment but they cannot be changed at our wish. They can be a major cause for variability in the responses. Other sources of variability are deviations around the set points of the controllable factors, plus sampling and measurement error. Furthermore, the system itself may be composed of parts that also exhibit variability. Disturbance, non controlled variables Wi, W2,..., Wq are immeasurable and their values are randomly changed in time. 

Feedforward Control A feedforward system uses measurements of disturbance variables to position the manipulated variable in such a way as to minimize any resulting deviation. The disturbance variables could be either measured loads or the set point, the former being more common. The feedforward gain must be set precisely to reduce the deviation of the controlled variable from the set point. 

Figure 8-40 includes two conventional feedback controllers Gcl controls Yi by manipulating (/, and Gc2 controls Y2 by manipulating U2. The output signals from the feedback controllers serve as input signals to the two decouplers T12 and T21. The block diagram is in a simplified form because the disturbance variables and transfer functions for the final control elements and sensors have been omitted. 

These decoupler design equations are very similar to the ones for feedforward control in an earlier section. In fact, decoupling can be interpreted as a type of feedforward control where the input signal is the output of a feedback controller rather than a measured disturbance variable. 

Step 1 Initial Controller Design The first step in MPC design is to select the controlled, manipulated, and measured disturbance variables. These choices determine the structure of the MPC system and should be based on process knowledge and control objectives. In typical... 

A process design is flexible if it can tolerate uncertainties in parameters and can handle disturbances. A flexibility index is a measure of the amount of uncertainty that can be tolerated with the desired process operation remaining feasible. A schematic of the flexibility index, 5, is shown in Fig. 8. Here, the two degrees of freedom represent uncertain parameters or disturbance variables, which have assumed upper and lower bounds. The feasible operating region lies within the cross-hatched area. The flexibility index is the fraction of the parameter range that still results... 

Controlled variables include product compositions (x,y), column temperatures, column pressure, and the levels in the tower and accumulator. Manipulated variables include reflux flow (L), coolant flow (QT), heating medium flow (Qb or V), and product flows (D,B) and the ratios L/D or V/B. Load and disturbance variables include feed flow rate (F), feed composition (2), steam header pressure, feed enthalpy, environmental conditions (e.g., rain, barometric pressure, and ambient temperature), and coolant temperature. These five single loops can theoretically be configured in 120 different combinations, and selecting the right one is a prerequisite to stability and efficiency. 

Plant-wide control is concerned with designing control systems for a large number of individual process units that may be highly interacting. A typical plant-wide control system will consist of many single-loop controllers as well as multi-variable controllers such as Model Predictive Control (MPC),1 10 and may involve thousands of measurements, hundreds to thousands of manipulated variables and hundreds of disturbance variables. Fortunately, a plant with a large number of processing units can be analysed as smaller clusters of units. 

Feedforward Control A feedforward system uses measurements of disturbance variables to position the manipulated variable in such a way as to minimize any resulting deviation. The disturbance... 

As briefly described above, the objective of the Sheet Forming Control Problem (SFCP) is to control the sheet thickness at 15 different points as uniformly as possible around different targets (yo). Thus, there are 15 controlled variables (CV s), which correspond to the thicknesses in the cross-direction, with the same relative weight (w). Moreover, this process has 9 manipulated variables (MV s) and 3 disturbance variables (DV s). The steady-state gain model, the sets within which the input and output variables are constrained and the relative weights of the output variables are given in the following equations ... 

Table 1. Feasible output ranges (AOIS) calculated for the SFCP = 12). The output variables for the original problem with 15 outputs, 9 inputs and 3 disturbance variables, are represented with y. The zone variables for the simplified square problem are represented with z.

As Figure 1 shows, the main stages of the proposed methodology are the preliminary data analysis, the identification of all process variables (outputs, inputs and disturbance variables), the transfer function model (i.e. the mathematical model that describes the... 

The governing equations for the disturbance variables are just the Boussinesq equations, (12 172), (12 176), and (12 177). However, in view ofthe fact that e 1, these equations... 

The governing linear stability equations for the disturbance variables are (in Cartesian component form)... 

Disturbance variable (DV). A DV affects the process in a known way but canuot be manipulated. 

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