Proportional-derivative control

Example 5.4 Derive the closed-loop transfer function of a system with proportional-derivative control and a first order process. 

When a proportional-only feedback controller is used, the ultimate gain is 2. Outline your procedure for finding the optimum value of tj, if a proportional-derivative controller is used. The optimum tj> wilt give the maximum value for the ultimate gain. 

A process has an openloop transfer function that is approximately a pure deadtime of D minutes. A proportional-derivative controller is to be used with a value of a equal to 0.1. What is the optimum value of the derivative lime constant Note that part of this problem involves defining what you mean by optimum. 

Compute the response of a PD (proportional-derivative) controller to a ramp change in the error e (i.e., e = at with a = constant). Sketch the contributions of the proportional and derivative actions separately. On the basis of this example discuss the anticipatory nature of the derivative control term. 

Proportional-derivative control. The addition of a derivative mode to a proportional controller results in faster action because the control signal is also proportional to the rate of change of the error ... 

Unfortunately, the ideal proportional-derivative control algorithm in Eq. 8-11 is physically unrealizable because it cannot be implemented exactly using either analog or digital controllers. For analog controllers, the transfer function in (8-11) can be approximated by... 

Ideal Proportional-Derivative Controller. The ideal proportional-derivative (PD) controller (cf. Eq. 8-11) is rarely implemented in actual control systems but is a component of PID control and influences PID control at high frequency. Its transfer function is... 

Figure 4.16 Proportional derivative controller response to a load disturbance...

Some of the inherent advantages of the feedback control strategy are as follows regardless of the source or nature of the disturbance, the manipulated variable(s) adjusts to correct for the deviation from the setpoint when the deviation is detected the proper values of the manipulated variables are continually sought to balance the system by a trial-and-error approach no mathematical model of the process is required and the most often used feedback control algorithm (some form of proportional—integral—derivative control) is both robust and versatile. 

Derivative mode This improves on the proportional-only control by responding solely to the rate of change of the deviation but not in any way to the actual value of the deviation. Derivative action is always used with proportional control. 

The temperature control was modeled by using these defining equations for a PID (Proportional-Integral-Derivative controller) algorithm ... 

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... 

Derivative action is never used by itself. The simplest implementation is a proportional-derivative (PD) controller. The time-domain equation and the transfer function of an "ideal" PD controller are ... 

As illustrated in Figure 29, the proportional only control mode responds to the decrease in demand, but because of the inherent characteristics of proportional control, a residual offset error remains. Adding the derivative action affects the response by allowing only one small overshoot and a rapid stabilization to the new control point. Thus, derivative action provides increased stability to the system, but does not eliminate offset error. 

Ashkin and Dziedzic (1977) used the radiation pressure force of a laser beam to levitate microdroplets with the apparatus presented in Fig. 15. A polarized and electro-optically modulated laser beam illuminated the particle from below. The vertical position of the particle was detected using the lens and split photodiode system shown. When the particle moved up or down a difference signal was generated then a voltage proportional to the difference and its derivative were added, and the summed signal used to control an electro-optic modulator to alter the laser beam intensity. Derivative control serves to damp particle oscillations, while the proportional control maintains the particle at the null point. 

There are two frequently used algorithms to determine the control action in a feedback control system for bioprocess control, an on-off (two-positioned) control, and a PID (proportional-integral-derivative) control. 

Proportional-lntegral-Derivative Control The most common algorithm for control action in the feedback loop of processing industries is the PID control, which is a combination of proportional action (P), integral action (1), and differential action (D). 

Proportional plus integral plus derivative control action... 

Let s consider a typical basic process control loop (Figure 2.1). A pressure-indicating transmitter (PIT) sends the pressure signal to a proportional integral derivative controller (PID), which sends a signal to the control valve to... 

The amplifier network provides signal conversion and suitable static and dynamic compensation for good positioner performance. Control from this block usually reduces to a form of proportional or proportional plus derivative control. The output from this block in the case of a pneumatic positioner is a single connection to the spring and diaphragm actuator or two connections for push/pull operation of a... 

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