Controller output

Many misconceptions exist about cascade control loops and their purpose. For example, many engineers specify a level-flow cascade for every level control situation. However, if the level controller is tightly tuned, the out-flow bounces around as does the level, regardless of whether the level controller output goes direcdy to a valve or to the setpoint of a flow controller. The secondary controller does not, in itself, smooth the outflow. In fact, the flow controller may actually cause control difficulties because it adds another time constant to the primary control loop, makes the proper functioning of the primary control loop dependent on two process variables rather than one, and requites two properly tuned controllers rather than one to function properly. However, as pointed out previously, the flow controller compensates for the effect of the upstream and downstream pressure variations and, in that respect, improves the performance of the primary control loop. Therefore, such a level-flow cascade may often be justified, but not for the smoothing of out-flow. 

Amplitude of controlled variable Output amplitude limits Cross sectional area of valve Cross sectional area of tank Controller output bias Bottoms flow rate Limit on control Controlled variable Concentration of A Discharge coefficient Inlet concentration Limit on control move Specific heat of liquid Integration constant Heat capacity of reactants Valve flow coefficient Distillate flow rate Limit on output Decoupler transfer function Error... 

ProportionaJ-plus-Integral (PI) Control Integral action eliminates the offset described above by moving the controller output at a rate proportional to the deviation from set point. Although available alone in an integral controller, it is most often combined with proportional action in a PI controller ... 

Proportional-plus-Integral-plus-Derivative (PID) Control The derivative mode moves the controller output as a function of the rate-of-change of the controlled variable, which adds phase lead to the controller, increasing its speed of response. It is normally combined... 

Other types of selective systems employ multiple final control elements or multiple controllers. In some applications, several manipulated variables are used to control a single process variable (also called split-range control). Typical examples include the adjustment of both inflow and outflow from a chemic reactor in order to control reactor pressure or the use of both acid and base to control pH in waste-water treatment. In this approach, the selector chooses from several controller outputs which final control element should be adjusted (Marlin, Process Control, McGraw-Hill, New York, 1995). 

In principle, ideal decouphng eliminates control loop interactions and allows the closed-loop system to behave as a set of independent control loops. But in practice, this ideal behavior is not attained for a variety of reasons, including imperfect process models and the presence of saturation constraints on controller outputs and manipulated variables. Furthermore, the ideal decoupler design equations in (8-52) and (8-53) may not be physically realizable andthus would have to be approximated. 

Introduction The model-based contfol strategy that has been most widely applied in the process industries is model predictive control (MFC). It is a general method that is especially well-suited for difficult multiinput, multioutput (MIMO) control problems where there are significant interactions between the manipulated inputs and the controlled outputs. Unlike other model-based control strategies, MFC can easily accommodate inequahty constraints on input and output variables such as upper and lower limits or rate-of-change limits. 

A key feature of MFC is that future process behavior is predicted using a dynamic model and available measurements. The controller outputs are calculated so as to minimize the difference between the predicted process response and the desired response. At each sampling instant, the control calculations are repeated and the predictions updated based on current measurements. In typical industrial applications, the set point and target values for the MFC calculations are updated using on-hne optimization based on a steady-state model of the process. Constraints on the controlled and manipulated variables can be routinely included in both the MFC and optimization calculations. The extensive MFC literature includes survey articles (Garcia, Frett, and Morari, Automatica, 25, 335, 1989 Richalet, Automatica, 29, 1251, 1993) and books (Frett and Garcia, Fundamental Process Control, Butterworths, Stoneham, Massachusetts, 1988 Soeterboek, Predictive Control—A Unified Approach, Frentice Hall, Englewood Cliffs, New Jersey, 1991). 

The discrete logic must have access to operational parameters such as controller modes. That is, the discrete logic must be able to switch a controller to manual, auto, or cascade. Furthermore, the discrete logic must be able to force the controller output to a specified value. 

Modern control systems permit the measurement device, the control unit, and the final actuator to be physically separated by several hundred meters, if necessary. This requires the transmission of the measured variable from the measurement device to the control unit, and the transmission of the controller output from the control unit to the final ac tuator. 

In each case, transmission of a single value in only one direction is required. Such requirements can be met by analog signal transmission. A span is defined for the value to be transmitted, and the value is basically transmitted as a percent of this span. For the measured variable, the logical span is the measurement span. For the controller output, the logical span is the range of the final actuator (e.g., valve fully closed to valve fully open). 

Analog alarms can be defined on measured variables, calculated variables, controller outputs, and the like. For analog alarms, the following possibilities exist ... 

The process controller is the master of the process-control system. It accepts a set point and other inputs and generates an output or outputs that it computes from a rule or set of rules that are part of its internal configuration. The controller output seiwes as an input to another controller or, more often, as an input to a final control element. The final control element is the device that affects the flow in the piping system of the process. The final control element seiwes as an interface between the process controller and the process. Control valves and adjustable speed pumps are the principal types discussed. 

Control-System Components The three principal elements of a control system are the sensing device which measures the error as the deviation from the set point, means for transmission and amphfi-cation of the error signal, and the control output device in the form of a seivo-operated valve. In the case of the direct-acting flyball governor (Fig. 29-18) these three elements are combined in the flyball element and the linkage that connects to the valve. 

This is a torque reference controller which controls the speed control output signal through the required torque reference signal and the d.c. link voltage. Its output torque reference is fed to the torque comparator (section i. ... 

Fig. 4.1 Block diagram of a closed-loop control system. R s) = Laplace transform of reference input r(t) C(s) = Laplace transform of controlled output c(t) B s) = Primary feedback signal, of value H(s)C(s) E s) = Actuating or error signal, of value R s) - B s), G s) = Product of all transfer functions along the forward path H s) = Product of all transfer functions along the feedback path G s)H s) = Open-loop transfer function = summing point symbol, used to denote algebraic summation = Signal take-off point Direction of information flow.

A generalized closed-loop control system is shown in Figure 4.22. The control problem can be stated as The control action u t) will be such that the controlled output c t) will be equal to the reference input r t) for all values of time, irrespective of the value of the disturbance input riit) . 

Algorithm A method of calculation that produces a control output by operating on an error signal or a time series of error signals. 

Proportional plus integral plus derivative action Proportional action provides a controller output proportional to the error signal. Integral action supplies a controller output which changes in the direction to reduce a constant error. Derivative action provides a controller output determined by the direction and rate of change of the deviation. When all these are combined into one controller (three-term or PID), there is an automatic control facility to correct any process changes. 

If Int (z/0.3 ) >= IntPrint Then Controls output interval IntPrint = IntPrint + 1 GoSub Output End If... 

Based on the shapes of the responses to step changes in controller output, and reasoning from the physical configuration of the extruder barrel, a reduced order dynamic model of the process was postulated. One can think of the Topaz program as order 80 (the number of nodes in the finite element subdivision), and the reduced model of order 4 (the number of dynamic variables). The figure below illustrates the model. 

LOAD, LOADl, LOAD2 = terms in the process model to accommodate non-zero steady state measurements (present values) at zero controller output, i.e. if the heaters are off (0 power) the temperature will not be 0. Also can be changed to represent undesired disturbances to the system affecting control. 

The identification of plant models has traditionally been done in the open-loop mode. The desire to minimize the production of the off-spec product during an open-loop identification test and to avoid the unstable open-loop dynamics of certain systems has increased the need to develop methodologies suitable for the system identification. Open-loop identification techniques are not directly applicable to closed-loop data due to correlation between process input (i.e., controller output) and unmeasured disturbances. Based on Prediction Error Method (PEM), several closed-loop identification methods have been presented Direct, Indirect, Joint Input-Output, and Two-Step Methods. 

In the basic conventional feedback control strategy the value of the measured variable is compared with that for the desired value of that variable and if a difference exists, a controller output is generated to eliminate the error. 

The simplest and, despite its several drawbacks, the most widely used type of control is the on/off control system. An example is a contact thermometer, which closes or opens a heater circuit. The designation on/off means that the controller output, or the manipulated variable (electric current) is either fully on or completely off. To avoid oscillations around the setpoint, the real on/off controller has built into it, a small interval on either side of the setpoint, within which the controller does not respond, and which is called the differential gap or deadzone. When the controlled variable moves outside the deadzone, the manipulated variable is set either on or off. This is illustrated in Fig. 2.30. Such shifts from the set point are known as offset. 

The simplest idea is that the compensation signal (actual controller output) is proportional to the error e(t) ... 

For all commercial devices, the proportional gain is a positive quantity. Because we use negative feedback (see Fig. 5.2), the controller output moves in the reverse direction of the controlled variable.1 In the liquid level control example, if the inlet flow is disturbed such that h rises above hs, then e < 0, and that leads to p < ps, i.e., the controller output is decreased. In this case, we of course will have to select or purchase a valve such that a lowered signal means opening the valve (decreasing flow resistance). Mathematically, this valve has a negative steady state gain (-Kv)2... 

A high proportional gain is equivalent to a narrow PB, and a low gain is wide PB. We can interpret PB as the range over which the error must change to drive the controller output over its full range.1... 

We expect a system with only a proportional controller to have a steady state error (or an offset). A formal analysis will be introduced in the next section. This is one simplistic way to see why. Let s say we change the system to a new set point. The proportional controller output, p = ps + Kce, is required to shift away from the previous bias ps and move the system to a new steady state. For p to be different from ps, the error must have a finite non-zero value.3... 

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