Process control derivative response

It is emphasized that drug activity is observed through a translation process controlled by cells. The aim of pharmacology is to derive system-independent constants characterizing drug activity from the indirect product of cellular response. 

Example 6.2 Derive the controller function for a system with a second order overdamped process and system response as dictated by Eq. (6-22). 

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. 

To illustrate the influence of each control mode, consider the control system responses shown in Figure 9.4. These curves illustrate the typical response of a controlled process for different types of feedback control after the process experiences a sustained disturbance. Without control the process slowly reaches a new steady state that differs from the desired steady state. The effect of proportional control is to speed up the process response and reduce the offset. The addition of integral control eliminates offset but tends to make the response more oscillatory. Adding derivative action reduces the degree of oscillation and the response time, ... 

Proportional-plus-integral control is the most generally useful control mode and therefore the one usually applied to automated process-control. Its major limitation is in processes with large dead-time and capacitance if reset time is faster than process dead-time, the controller-response changes are faster than the process, and cycling results. In these cases, derivative control is beneficial. 

Myoelectric control derives it name from the electromyogram (EMG), which it uses as a control input. When a muscle contracts, an electric potential (the EMG) is produced as a by-product of that contraction. If surface electrodes are placed on the skin near a muscle, they can detect this signal (Fig. 32.26). The signal can then be electronically amplified, processed, and used to control a prosthesis. While the intensity of the EMG increases as muscle tension increases, the relationship is a complex nonlinear process that depends on many variables, including the position and configuration of the electrodes (Heckathome and Childress, 1981). Although the EMG is nonlinear it is broadly monotonic, and the human operator perceives this response as more or less linear. 

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. 

The type of control signal response to a step setpoint change encountered with a stable process under feedback control would be familiar to a process engineer. The first key feature is the immediate step change in the control signal when the setpoint value is changed. It is common practice to place the derivative term of the PID controller in the feedback loop so that it only acts on the filtered process variable to avoid derivative kick (see Figure 6.2). 

Simple first order plus delay models for this process were derived firom step response tests. For controlling the temperature of the outlet water stream, the manipulated input variable is the steam valve position and the process output variable is the outlet water temperature, measured at one of three thermocouples located at different distances from the tank outlet. The tests involved introducing a step change in steam valve position, with the temperature controller in manual, and observing the response in the outlet water temperature at each of the three thermocouples. Simple graphical methods were used to calculate the parameters of the first order plus delay models. 

One final point about closed-loop process control Economic considerations dictate that to derive optimum benefits, processes must invariably be operated in the vicinity of constraints. A good control system must drive the process toward these constraints without actually violating than. In a polymerization reactor, the initiator feed rate may be manipulated to control monomer conversion or Mj, however, at times when the heat of polymerization exceeds the heat transfer capacity of the kettle, the initiator feed rate must be constrained in the interest of thermal stability. In some instances, there may be constraints on the controlled variables as well. Identification of constraints for optimized operation is an important consideration in control system design. Operation in the vicinity of constraints poses problems because the process behavior in this region becomes increasingly nonhnear. In many cases, the capabihty to control polymerizations is severely limited by the state of the art in measurement instrumentation. In other cases, the dynamic response of the instruments dictates the design strategy for the process. 

In most controllers, derivative action does not distinguish between measurement and set point. The purpose of derivative is to speed the response of the closed loop, but the set point lies outside the loop. The controlled variable cannot change instantaneously, because of the lags inherent in the process. But it is normal to introduce set-point changes instantaneously, which derivative action amplifies into gross output... 

Control algorithms We have discussed that in closed-loop control systems a corrective action is taken by the controller in response to feedback from a transducer. The exact corrective action depends on the algorithm which has been developed. The simplest control approach is a two position control which turns the control element on and off based on the monitored value of the output. With an on/off strategy, the process value will typically oscillate above and below the set point. The most common controller is the PID (proportional, integral, and derivative) loop controller which is able to detect an early trend, adjust quickly, and prevent an over-correction. A PID controller can maintain temperatures within 1°F. The controller provides the means to define the control algorithm by assigning a constant for each of the three control modes. Typically, most of the adjustment is accomplished with the proportional control element, with the control action, u be-... 

The use of decibels merely results in a rescaling of the Bode plot AR axis. The decibel unit is employed in electrical communication and acoustic theory and is seldom used today in the process control field. Note that the MATLAB bode routine uses decibels as the default option however, it can be modified to plot AR results, as done in Fig 14.2. In the rest of this chapter, we only derive frequency responses for simple transfer function elements (integrator, first-order, second-order, zeros, time delay). Software should be used for calculating frequency responses of combinations of these elements. 

These expressions can be derived by the interested reader. The resonant frequency co is that frequency for which the sinusoidal output response has the maximum amplitude for a given sinusoidal input. Eqs. (14-25) and (14-26) indicate how co and (A/ )max depend on This behavior is used in designing organ pipes to create sounds at specific frequencies. However, excessive resonance is undesirable, for example, in automobiles, where a particular vibration is noticeable only at a certain speed. For industrial processes operated without feedback control, resonance is seldom encountered, although some measurement devices are designed to exhibit a hmited amount of resonant behavior. On the other hand, feedback controllers can be tuned to give the controlled process a slight amount of oscillatory or underdamped behavior in order to speed up the controlled system response (see Chapter 12). 

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