Derivative control action

We certainly want to respond very differently if the temperature of a chemical reactor is changing at a rate of 100°C/s as opposed to l°C/s. In a way, we want to "project" the error and make corrections accordingly. In contrast, proportional and integral controls are based on the present and the past. Derivative controller action is based on how fast the error is changing with time (rate action control). We can write... 

To reduce derivative kick (the sudden jolt in response to set point changes), the derivative action can be based on the rate of change of the measured (controlled) variable instead of the rate of change of the error. One possible implementation of this idea is in Fig. 5.3. This way, the derivative control action ignores changes in the reference and just tries to keep the measured variable constant.2... 

Proportional plus integral plus derivative control action... 

In a well-engineered system, measurement noise is unlikely to affect the performance of a PI controller significantly (Section V.A.2), but it may limit the use of derivative control action and will certainly limit the performance of advanced control schemes that attempt to approach ideal control (Section V.A.5). Our approach to PID control has been to optimize PI controllers and leave the possible benefit of derivative action to the commissioning engineers. 

Williams et al. (Wl), describe the results of studies of the automatic control of continuous fractional distillation. These studies were made on an analog computer which could simulate a five-plate tower. The effects of column design, varying feed rate, imperfect sampling, and quality of feed and reflux on controllability were evaluated. An earlier article by Rose and Williams (R2) on the same system compares various schemes for controlling fractionation columns. One interesting conclusion is that derivative control action cannot improve the control for any of the various combinations of measurement and regulation that were studied. 

Minimizing the overall phase angle of a typical process system, maximizes the frequency at phase crossover and hence maximizes the response speed of the system. Large phase lags in process components, for example resulting from distance-velocity lags, can be counteracted by the phase lead characteristic of derivative control action. 

With the presence of the derivative term, (de/dt), the PID controller anticipates what the error will be in the immediate future and applies a control action which is proportional to the current rate of change in the error. Due to this property, the derivative control action is sometimes referred to as anticipatory control. 

The major drawbacks of the derivative control action are the following ... 

Assuming again for simplicity that Gm = Gf = 1, the closed-loop response of a first-order system with derivative control action is given by... 

Equation (14.27) leads to the following observations on the effects that the derivative control action has on the closed-loop response of a system ... 

It is very instructive to examine the effect of the derivative control action on the response of a second-order system. Assuming... 

Combination of the three control modes leads to a closed-loop response which has in general the same qualitative dynamic characteristics as those resulting from PI control alone. Let us now describe the main benefit introduced by the derivative control action. 

Figure 14.10 summarizes the effect of a PID controller on the response of a controlled process. Notice that although increasing Kc leads to faster responses, the overshoot remains almost the same and the settling time is shorter. Both are results of the derivative control action. 

Let us now examine how the response of a normal, uncontrolled process is changed when a simple proportional, integral, or derivative feedback controller is incorporated. In this section we consider only the proportional controller and its effect on the most commonly encountered first- and second-order systems. The effects of integral and derivative control actions will be studied in the following two sections. 

Although proportional control can be used alone, this is almost never the case for integral or derivative control actions. Instead, proportional-integral (PI) and proportional-integral-derivative (PID) are the usual controllers employing integral and derivative modes of control. 

What are the relative advantages and disadvantages of the proportional, integral, and derivative control actions What are their characteristic effects on the closed-loop response of a process ... 

Use a PID controller to increase the speed of the closed-loop response and retain robustness. The PI eliminates the offset but reduces the speed of the closed-loop response. For a multicapacity process whose response is very sluggish, the addition of a PI controller makes it even more sluggish. In such cases the addition of the derivative control action with its stabilizing effect allows... 

Derivative control action is also referred to as rate action, preact, or anticipatory control. Its function is to anticipate the future behavior of the error signal by considering its rate of change. Derivative action is never used alone, but in conjunction with proportional and integral control. Derivative control is used to... 

Figure 24.7. The proportional-plus-derivative controller. Derivative action is accomplished by a shunt capacitor C across Rf. When deviation from the setpoint is rapid, the low reactance of the capacitor causes less negative feedback—hence, greater amplifier gain. The derivative time resistor Ra allows adjustment of the magnitude of derivative control action to a given rate of change of the error signal. Courtesy of the Foxboro Company.

Derivative control action (D) can improve the response of slow systems when coupling parallel to proportional control by adding an effect proportional to the time derivative of the error. This way some disadvantageous effects of large load changes and the maximum error can be reduced. 

Selection of Control Systems In the operation of control systems stability is required. Operation is stable when continuous cycling will not occur. Instability could be the consequence of the increase in the overall gain of the controller above a maximum value. The overall gain of the controller is the product of gain terms in a closed loop. The role of the time lag may also be considered. Different stabihty aiteria have been elaborated and various rules developed. Integral control and derivative control action can improve the stability of systems added to proportional control. The final performance of a system is affected by the characteristics of the process to be controlled, by the operational characteristics of the controller used, and by the nature of the disturbances to be expected. 

Both numerical and explicit implementations of the DMC algorithms are researched. In case of the numerical DMC algorithm, it derives control action by solving a quadratic optimization problem at each iteration. It is an approach often used in practical applications. However, from the computational point of view, it is much more complicated than an explicit control algorithm. As a consequence, the numerical DMC control algorithm is hard to test using the conventional SWIFI approach. Thus, a new SWIFI system is proposed to address this problem. 

Derivative control action is also referred to as rate action, preact, or anticipatory control. Its function is to anticipate the future behavior of the error signal by computing its rate of change thus, the shape of the error signal influences the controller output. Derivative action is never used alone, but in conjunction with proportional and integral control. Derivative control is used to improve the dynamic response of the controlled variable by decreasing the process response time. If the process measurement is noisy, however, derivative action will ampHfy the noise unless the measurement is filtered. Consequently, derivative action is seldom used in flow controllers because flow control loops respond quickly and flow measurements tend to be noisy. In the chemical industry, there are more PI control loops than PID. 

Response curves for sampled loops are made of steps. The rate of rise of even a small step is extremely high therefore derivative control action on a sampled signal produces pulsing of the manipulated variable. This pulsing cannot contribute much to the closed-loop response, because sampling prevents the effect of such action from being seen-consequently the manipulated variable is driven severely without cause. Derivative is therefore of little value in the sampled loop. 

The function of derivative control action is to anticipate the future behavior of the error signal by considering its rate of change. In the past, derivative action was also referred to as rate action, pre-act, or anticipatory control For example, suppose that a reactor temperature increases by 10 °C in a short period of time, say, 3 min. This clearly is a more rapid increase in temperature than a 10 °C rise in 30 min, and it could indicate a potential runaway situation for an exothermic reaction. If the reactor were under manual control, an experienced plant operator would anticipate the consequences and quickly take appropriate corrective action to reduce the temperature. Such a response would not be obtainable from the proportional and integral control modes discussed so far. Note that a proportional controller reacts to a deviation in temperature only, making no distinction as to the time period over which the deviation develops. Integral control action is also ineffective for a sudden deviation in temperature, because the corrective action depends on the duration of the deviation. 

Elimination of Derivative Kick. When a sudden set-point change is made, the PID control algorithms in Eq. 8-26 or Eq. 8-28 will produce a large immediate change in the output due to the derivative control action. For digital control algorithms. 

Step 1. After the process has reached steady state (at least approximately), eliminate the integral and derivative control action by setting ij) to zero and t/ to the largest possible value. 

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