Deadbanding

A three-state controller is used to drive either a pair of independent on/off actuators such as heating and cooling valves, or a bidirectional motorized actuator. The controller is actually two on/off controllers, each with deadband, separated by a dead zone. When the controlled variable lies within the dead zone, neither output is energized. This controller can drive a motorized valve to the point where the manipulated variable matches the load, thereby avoiding cychng. 

One operational problem with analog alarms is that noise in the variable can cause multiple alarms whenever its value approaches a limit. This can be avoided by defining a deadband on the alarm. For example, a high alarm would be processed as follows ... 

Return to normal. The high-alarm return to normal is generated when the value is less than or equal to the high alarm limit less the deadband. 

As the degree of noise varies from one input to the next, the deadband must be individually configurable for each alarm. 

When a process error is below certain tolerable deadband, the controller ceases modifying output. This is referred to as gap action. 

This effect was explored by using a PI controller based on concentration around a tank with = 9 s and = 171 s as above. Again, there is no rea.son to expect the conclusions to be sensitive to the particular mixing conditions. The definition of deadband given leaves some ambiguity as to the valve behavior. Two models were considered for a unit deadband error ... 

Numerical experiments (Walsh, 1993) indicate that the peak-to-peak deviation of the exit concentration can be bounded, for fairly tightly tuned controllers, by calculating the response of the exit concentration to a reagent valve exhibiting a square wave oscillation with peak-to-peak amplitude equal to the deadband error. The exit concentration variation can therefore be estimated as... 

If it is desired to evaluate advanced control schemes, the models used in this work should be regarded as generating an upper bound on practically achievable performance further work is required to generate models suitable for this purpose. At a minimum, the performance of advanced control algorithms should be checked in the presence of correlated noise and actuator deadband error, and an improved model of the probe respon.se is likely to be needed. 

PRSW - Pressure switch, hermetically sealed, fixed deadband, stainless steel, snap action switch... 

The valve positioner, which is usually contained in its own box and mounted on the side of the valve actuator, is designed to control the valve stem position at a prescribed position in spite of packing friction and other forces on the stem. The valve positioner itself is a feedback controller that compares the measured with the specified stem position and makes adjustments to the instrument air pressure to provide the proper stem position. In this case, the setpoint for the valve positioner can be a pneumatic signal coming from an l/P converter or the 4-20 mA analog signal coming directly from the controller. A valve with a deadband of 25% can provide flow rate precision... 

Time Constant Valve Deadband or Turndown Ratio,... 

The key to effective troubleshooting is expressed in the old adage, divide and conquer. It is important to locate the portion of the control loop hardware that is causing the poor performance the hnal control element, the sensor system, the controller, or the process. The place to start is to test each system separately to determine whether that portion of the control loop is operating properly. The hnal control element can be evalnated by applying a series of input step tests. That is, the input to the hnal control element, which is normally set by the controller, can be manually adjusted. The test allows the determination of the dynamic response and deadband of the actuator system. If the performance in these two areas is satisfactory, there is no need to evaluate the actuator system further. 

Even if the manipulated variable seems to follow the controller ontput, there could be a problem with the actuator. Estimates of the actuator deadband and dynamic response are required to determine if the actuator system is performing properly (both of which can be determined by a block sine wave test). This test is shown in Figure 15.21. A block sine wave is a series of eqnally sized step changes that approximate a sine wave. For the test shown in the figure, the amplitude... 

FIGURE 15.21 Results of a series of block sine wave tests to determine the deadband of the actuator. Note that the signal to the actuator and the measured value of the flow rate are plotted on different scales. 

Once the deadband and time constant of the actuator have been determined, the performance of the actuator can be assessed. The deadband for valves with positioners typically ranges from... 

Low instrument air pressure Wet or dirty instrument air Excessive deadband ... 

After each of the components has been evaluated and corrected wherever possible, the closed-loop system should be checked. From an overall point of view, there are three general factors that affect the closed-loop performance of a control loop (1) the type and magnitude of disturbances, (2) the lag associated with the components that compose the control loop, and (3) the precision to which each component of the control loop performs. Actuator deadband affects the variability in the controlled variable. The addition of lag to a control loop (e.g., sensor filtering) results in slower disturbance rejection, which can increase the variability in the controlled variable. Disturbance magnitude directly affects variability. 

The performance of a closed-loop system can be assessed by the settling time, closed-loop deadband, and the variability of the controlled variable evaluated over an extended period of time. The settling time and the closed-loop deadband can be determined using a closed-loop block sine wave test. For a closed-loop block sine wave test, the setpoint for the control loop is applied in the form of a block sine wave, and the amplitude of the block sine wave is varied until the deadband is determined. During these tests, the settling time of the controller can also be estimated. An accurate determination of the variability of a controlled variable generally requires an extended period of operation. An evaluation of the variability based on a short period of time may not be representative of true system performance. 

The closed-loop deadband is an indication of the variability in the controlled variable that results from the combined effects of actuator deadband, sensor noise, and resolution of the A/D and D/A converters. The closed-loop settling time is an indication of the combined lags of the control loop components. The closed-loop performance assessment is a means of determining whether all the major problems within a control loop have been rectified. 

Step 1. Determine the deadband of the final control element using a series of block sine wave tests. Result the deadband of the final control element was less than 0.4%, and the dynamic response time of the final control element was 2 s therefore, the final control element was found to be functioning properly. 

Final elements must provide the desired capacity with the required precision of flow throttling over the desired range, usually 10% to 95% of maximum flow. The valve characteristic should provide a linear closed-loop gain, except choose linear or quick-opening characteristics for valves that are normally closed but must open quickly. Select the valve failure position for safety. The valve body should satisfy such requirements as required flow at 0% stem position, plugging, pressure drop, or flashing. The nonideal final element behavior, such as friction and deadband, should be small, as required by each application. Control valves should have manual bypass and block valves to allow temporary valve maintenance when short process interruptions are not acceptable. However, the bypass should never compromise safety interlock systems. 

Chapter 22 provides equations for typical process controllers and control valve dynamics. The controllers considered are the proportional controller, the proportional plus integral (PI) controller and the proportional plus integral plus derivative (PID) controller. Integral desaturation is an important feature of PI controllers, and mathematical mc els are produced for three different types in industrial use. The control valve is almost always the final actuator in process plan. A simple model for the transient response of the control valve is given, which makes allowance for limitations on the maximum velocity of movement. In addition, backlash and velocity deadband methods are presented to model the nonlinear effect of static friction on the valve. 

Modelling static friction the velocity deadband method... 

It is interesting to compare the backlash description of static friction with the velocity deadband model. Equation (22.56) was programmed for the velocity deadband method, while equations (22.58) and (22.59) were programmed for the backlash description. The half-deadband/half-backlash width, b, was chosen as the largest likely value of 0.05. The two models were subjected to a controller output consisting of a damped oscillatory output of period 150 seconds. The exciting... 

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