31594165 Controller Tuning 3f2520

CONTROLLER TUNING: Tuning a control loop is the adjustment of its control parameters (gain/proportional band, integral gain/reset, derivative gain/rate) to the optimum values for the desired control response. If the PID controller parameters (the gains of the proportional, integral and derivative ) are chosen incorrectly, the controlled process input can be unstable, i.e. its output diverges, with or without oscillation. The process of tuning can vary from a trial-and-error attempt to find suitable control parameters for “good” control to an elaborate optimization calculation based on a model of the process. Selection of Controller Modes Consider the typical system as shown in fig 1.

All the four types of controllers (P, PD, PI and PID) are taken into consideration. They are subjected to unit step change in load and the response was drawn as shown in fig 2. Nature of the response from different type of controller is described now. PROPORTIONAL CONTROL. As shown in Fig.2, proportional control produces an overshoot followed by an oscillatory response, which levels out at a value that does not equal the set point; this ultimate displacement from the set point is the offset. PROPORTIONAL-DERIVATIVE CONTROL. For this case the response exhibits a smaller overshoot and a smaller period of oscillation compared to the response for proportional control. The offset that still remains is less than that for proportional control. PROPORTIONAL-INTEGRAL CONTROL. In this case, the response has about the same overshoot as proportional control, but the period is larger; however, the response returns to the set point (offset = 0) after a

relatively long settling time. The most beneficial influence of the integral action in the controller is the elimination of offset. PROPORTIONAL-INTEGRAL-DERIVATIVE CONTROL. As one might expect, the use of PID control combines the beneficial features of PD and PI control. The response has lower overshoot and returns to the set point more quickly than the responses for the other types of controllers.

CONCLUSIONS: 1. Integral action, which is present in PI and PID controllers, eliminates offset. The addition of derivative action speeds up the response by contributing to the controller output a component of the signal that is proportional to the rate of change of the process variable. 2. For simple, low-order (first or second-order) processes that can tolerate some offset, P or PD control is satisfactory. For processes that cannot tolerate offset and are of low order, PI control is required. For processes that are of high-order (those with transport lag or many first-order lags in series), PID control is needed to prevent large overshoot and long settling time.

Criteria for Good Control: 1. 2. 3. 4.

Should have the minimum overshoot of the response to unit step change in load. Should have the quarter decay ratio. Minimum rise time Minimum settling time

METHODS OF TUNING: 1. OPEN LOOP METHOD (C-C method): It is also known as Cohen and Coon method of tuning. In open loop method the control action is removed from the controller by placing it in manual mode and an open-loop transient is induced by a step change in the signal to the valve. This method was proposed by Cohen and Coon (1953) and is often used as an alternative to the Z N method. The step change to the valve is conveniently provided by the output from the controller, which is in manual mode. The response of the system (including the valve, process, and measuring element) is called the process reaction curve. Figure.3 shows a typical control loop in which the control action is removed and the loop opened for the purpose of introducing a step change (M/s) to the valve. The C-C method is summarized in the following steps: 1. After the process reaches steady state at the normal level of operation, switch the controller to manual. In a modem controller, the controller output will remain at the same value after switching as it had before switching. 2. With the controller in manual, introduce a small step change in the controller output that goes to the valve and record the transient, which is the process reaction curve (Fig. 4)

3. Draw a straight line tangent to the curve at the point of inflection, as shown in

Fig. 4. The intersection of the tangent line with the time axis is the apparent transport lag (Td); the apparent first-order time constant (7) is obtained from T = B,IS

where B, is the ultimate value of B at large t and S is the slope of the tangent line. The steady-state gain that relates B to M in Fig. 3 is given by K, = B,IM

4. Using the values of K,, T, and Td from step 3, the controller settings are found from the relations given in Table in book.

Ziegler-Nichols Method(Z-N): The method is described as a closed-loop method because the controller remains in the loop as an active controller in automatic mode. The rules are presented below, and are in the form that one would use for actual application to a-real process. 1) After the process reaches steady state at the normal level of operation, remove

the integral and derivative modes of the controller, leaving only proportional control. On some PID controllers, this requires that the integral time (~1) be set to its maximum value and the derivative time (7~) to its minimum value. On modern controllers (microprocessor-based), the integral and derivative modes can be removed completely from the controller. 2) Select a value of proportional gain (K,), disturb the system, and observe the

transient response. If the response decays, select a higher value of K, and again observe the response of the system. Continue increasing the gain in small steps until the response first exhibits a sustained oscillation. The value of gain and the period of oscillation that correspond to the sustained oscillation are the ultimate gain (K,,) and the ultimate period (Pu). 3) From the values of K,, and P, found in the previous step, use the Ziegler- Nichols

rules given in Table 19.1 to determine controller settings (Kc,TI,TD). controller settings. The Z-N settings should be considered as only approximate settings for satisfactory control. Fine tuning of the controller settings is usually required to get an improved control response.

The experimental determination of K,, and P, described in step 2 canbe replaced by a computation using frequency response methods if an accurate model of the process, valve, and measuring element is known.

PRECAUTIONS TO TAKE IN APPLYING THE Z-N METHOD. Some discussion is needed to avoid some pitfalls in applying step 2 of the Z-N method to obtain K cu and P, . These precautions are concerned with the type and size of the disturbance that induces the response and with the avoidance of using a limit cycle as the indication that the system is on the threshold of instability. The simplest way to introduce a disturbance is to move the set point away from the control variable for a short time and then return the set point to its original value. This procedure, which is equivalent to introducing a pulse function in the error, causes the system to respond and yet stay within a narrow band surrounding the normal operating point of the process. An alternate type of disturbance would be to introduce a small step change in set point. If step changes in set point are used to induce transients, the successive step changes should alternate around the normal operating point of the process. It is also important to make the disturbance as small as possible, especially as the gain of the controller is increased, so that the valve and other components do not exceed their physical limits. When the valve moves to its limits during a closed-loop transient, we say that the valve saturates. Under these conditions, a sustained oscillation occurs. which is called a limit cycle. If the limits of the valve (e.g., 3 psi to 15 psi) are reached repeatedly during the oscillatory response, one has a limit cycle and the controller gain and period should not be used to determine controller settings. It is for this reason step 2 states that K, should be increased in small steps until the response first exhibits a sustained oscillation.