Error, integrated with feedback control

The PID controller is the most commonly used feedback controller in industry, with three tunable parameters as stated previously. The integral component ensures that the tracking error, E t), is asymptotically reduced to zero, whereas the derivative component imparts a predictive capability, potentially enhancing the performance. Despite its apparent simplicity, the subject of PID controller tuning has been discussed in several textbooks and thousands of research papers since the landmark work of Ziegler and Nichols (1942). In practice, despite these developments, most PID controllers are tuned as PI controllers for several reasons. 

The state feedback controller with integration that includes the static feedforward for calculating compressor air flow rate state error minimizes error between desired and actual air flow rate through the compressor. 

Nearly all control loops utilize some form of feedback control. The most prevalent type of controller is a proportional-integral (PI). A PI basically provides a controller output that is the sum of a contribution that is proportional to the pH error and the integral of the pH error, where the error is the difference between the pH set point and the measurement. If the pH loop is on a vessel where there is a large time constant that provides a smooth transition in pH, it is beneficial to include rate action to form a proportional-integral-derivative (PID) controller so that there is a contribution to the controller output that is proportional to the rate of change of the pH or the control error. If the set point is on a flat part or a bend in the curve, rate is particularly effective at dealing with the drastic acceleration associated with an excursion to the steep portion of the curve. 

If all the state variables are not measured, an observer should be implemented. In the Figure 14, the jacket temperature is assumed as not measured, but it can be easily estimated by the rest of inputs and outputs and based on the separation principle, the observer and the control can be calculated independently. In this structure, the observer block will provide the missing output, the integrators block will integrate the concentration and temperature errors and, these three variables, together with the directly measured, will input the state feedback (static) control law, K. Details about the design of these blocks can be found in the cited references. 

In this particular example turbine speed control was taking place. The closed loop feedback is turbine speed in rpm as measured by an optical pickup on the generator box (nearly instantaneous). In this test, the experimental speed controller and the simulated speed controller (in both models), used a proportional gain of 0.001 and an integral gain of 0.001 x 0.75 with an input of speed error in rpm and output in fuel valve %. For the experiment presented, the fuel flow rate in grams per second... 

The mean value of error may be expected to increase monotonically as simacc increases while the computation time may be expected to decrease monotonically as simacc increases. The control objective is therefore to maintain a value of error that is Just small enough to prevent serious noise problems. The precise relationship between simacc and error is unclear and will vary from system to system and integrator to integrator. As in any feedback scheme with a poorly defined system model, the feedback system must be suitably conservative to avoid instability. The scheme below has been found to be effective in extensive trials. 

It must be remembered that liquid-level processes such as this are non-self-regulatlng. The controlled variable will consequently drift unless feedback is applied. Since integral feedback may not be used alone, because instability would result, a two-mode controller is always used. In the steady state, feedwater flow will always equal steam flow, so the output of the level controller will seek the bias appUed to the computation. If the controller Is to be operated at about 50 percent output, that bias must be 0.5, as indicated in the formula. The controller does not have to integrate its output to the entire extent of the load change with a forward loop in service, but need only trim out the change in error of the computation during that interval. 

The anti reset-windup technique discussed above is known as external reset feedback. For most applications either it, or the modification mentioned below, is our preferred scheme. It has the disadvantage that the controller output signal, commonly labeled valve position, is really different from the actual position. It differs by the product of the error signal times the proportional gain. Lag in the reset circuit may cause further error. A modification therefore is introduced by some vendors, particularly in the newer microprocessor controls. This consists of setting the reset time equal to zero when the controller is overridden. This technique is sometimes called integral tracking. It should not be used with auto overrides. 

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