Variables, controllable input, output

A model of a dynamic system is usually expressed in the state space in the form of differential equations which combine time-variable controlled inputs to the object, the current state of the system and output from the system. For sampled systems (as implemented in most system modelling and control applications) the corresponding difference time-state equations... 

Ratio and Multiplicative Feedforward Control. In many physical and chemical processes and portions thereof, it is important to maintain a desired ratio between certain input (independent) variables in order to control certain output (dependent) variables (1,3,6). For example, it is important to maintain the ratio of reactants in certain chemical reactors to control conversion and selectivity the ratio of energy input to material input in a distillation column to control separation the ratio of energy input to material flow in a process heater to control the outlet temperature the fuel—air ratio to ensure proper combustion in a furnace and the ratio of blending components in a blending process. Indeed, the value of maintaining the ratio of independent variables in order more easily to control an output variable occurs in virtually every class of unit operation. 

In the context of chemometrics, optimization refers to the use of estimated parameters to control and optimize the outcome of experiments. Given a model that relates input variables to the output of a system, it is possible to find the set of inputs that optimizes the output. The system to be optimized may pertain to any type of analytical process, such as increasing resolution in hplc separations, increasing sensitivity in atomic emission spectrometry by controlling fuel and oxidant flow rates (14), or even in industrial processes, to optimize yield of a reaction as a function of input variables, temperature, pressure, and reactant concentration. The outputs ate the dependent variables, usually quantities such as instmment response, yield of a reaction, and resolution, and the input, or independent, variables are typically quantities like instmment settings, reaction conditions, or experimental media. 

In the case of the ship shown in Figure 1.3, the rudder and engines are the control inputs, whose values can be adjusted to control certain outputs, for example heading and forward velocity. The wind, waves and current are disturbance inputs and will induce errors in the outputs (called controlled variables) of position, heading and forward velocity. In addition, the disturbances will introduce increased ship motion (roll, pitch and heave) which again is not desirable. 

The use of block diagrams to illustrate cause and effect relationship is prevalent in control. We use operational blocks to represent transfer functions and lines for unidirectional information transmission. It is a nice way to visualize the interrelationships of various components. Later, they are crucial to help us identify manipulated and controlled variables, and input(s) and output(s) of a system. 

At time tb the measured variable increases by 100°F, or 50%, of the measured variable span. This 50% controller input change causes a 100% controller output change due to the controller s proportional band of 50%. The direction of the controller output change is decreasing because the controller is reverse-acting. The 100% decrease corresponds to a decrease in output for 15 psi to 3 psi, which causes the control valve to go from fully open to fully shut. 

At time tj, the measured variable decreases by 50°F, or 25%, of the measured variable span. The 25% controller input decrease causes a 50% controller output increase. This results in a controller output increase from 3 psi to 9 psi, and the control valve goes from fully shut to 50% open. 

A process, or activity, can be defined as a transfer function with one or more inputs, outputs, controls, and resources that together all enable the variables to gain data and then fire. 

The external processes (boundary fluxes) can be combined into four pairs of generalized exchange fluxes that is (a) input/output by streams, rivers, or ground-water, (b) air-water exchange, (c) sediment-water exchange, (d) exchange with adjacent water compartments. If the box represents a pond or lake as a whole, flux (d) does not exist. The fluxes into the system are controlled by external parameters such as the concentration in the inlets, the atmospheric and the sedimentaiy concentrations. These concentrations can be constant or variable with time. 

Control based on neural network. Similar to fuzzy logic modeling, neural network analysis uses a series of previous data to execute simulations of the process, with a high degree of success, without however using formal mathematical models (Chen and Rollins, 2000). To this goal, it is necessary to define inputs, outputs, and how many layers of neurons will be used, which depends on the number of variables and the available data. 

A step change is applied to the manipulated variable (controller output, which is an input to the process). The step changes are usually 5 to 10%. The step time should be long enough for the manipulated variable (system input) to reach a new steady state. 

With the outputs y and M, using the reduced-order model (7.38), a multi-variable input-output linearizing controller with integral action (Daoutidis and Kravaris 1994) was designed for the product purity and reactor holdup, requesting a decoupled first-order response ... 

They are multivariable in nature, and there are interactions which exist among the various control and output variables, making a simplistic single input-output (SISO) strategy somewhat hazardous if not inefficient. 

In this study we identify an SMB process using the subspace identification method. The well-known input/output data-based prediction model is also used to obtain a prediction equation which is indispensable for the design of a predictive controller. The discrete variables such as the switching time are kept constant to construct the artificial continuous input-output mapping. With the proposed predictive controller we perform simulation studies for the control of the SMB process and demonstrate that the controller performs quite satisfactorily for both the disturbance rejection and the setpoint tracking. 

In order to solve the first principles model, finite difference method or finite element method can be used but the number of states increases exponentially when these methods are used to solve the problem. Lee et u/.[8] used the model reduction technique to reslove the size problem. However, the information on the concentration distribution is scarce and the physical meaning of the reduced state is hard to be interpreted. Therefore, we intend to construct the input/output data mapping. Because the conventional linear identification method cannot be applied to a hybrid SMB process, we construct the artificial continuous input/output mapping by keeping the discrete inputs such as the switching time constant. The averaged concentrations of rich component in raffinate and extract are selected as the output variables while the flow rate ratios in sections 2 and 3 are selected as the input variables. Since these output variables are directly correlated with the product purities, the control of product purities is also accomplished. 

Hot-melt extrusion also requires other components to be scaled up in size as the extruder is scaled up in size. Typical components include multiple powder and liquid feeders, a chiller, a take-off cooling belt unit, and a control panel(s). Proper sizing of all components to achieve control of the process at each step is critical, especially because of the interrelationship of individual component feeds into the extruder and the resulting quality of the final extrudate. Variability on inputs translates into product variability on output from the extruder owing to its continuous principle of operation. 

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