Overview of the PID Controller

Generally a PID controller has three control terms; Proportional, Integral and Derivative. The proportional term is a simple gain factor and provides a means of influencing the rate of adjustment of the manipulated variable. For most process applications the proportional control action has a very straightforward effect on the performance of the controller, especially in terms of the influence of this term on the overshoot and rise time of the output response to a step change of reference. This control action is capable of reducing the offset error but it does not provide a zero offset in typical process applications involving a Type 0 plant transfer function.

The second term in the PID controller is the integral action term. The main advantage of this control action is its influence on the final steady state error value, although it adjusts the manipulated variable in a slower manner than pure proportional action and the integral action can have a destabilising effect in terms of the dynamic response of the closed- loop system. Integral action is capable of bringing the steady state output value to the desired set point with zero offset for a plant that shows linear behaviour and may be described by a Type 0 transfer function.

In the PID controller one important issue that arises with the integral action is the phenomenon of “Integral Windup”. This problem is associated with saturation effects and occurs when the integral action continues to integrate the error (in a positive or negative direction) but the manipulated variable is unable to control the process variable. This is because the control valve or other form of actuator reaches a hard limit at one end or the other of its travel (0% or 100% in the case of a control valve).

There are many different anti-windup strategies which have been suggested in order to avoid this situation. As mentioned in a number of papers (Bohn & Atherton 1994;Bohn & Atherton 1995), there are three commonly used methods or schemes that can reduce or prevent the integral windup problem.

The first scheme involves clamping the integrator output at specific a minimum and maximum value. This scheme is normally referred to as a “Limited Integrator”

approach. The saturation values usually correspond to the hard limit of the actuator.

The main idea of this simplest scheme is that the integrator will stop integrating when the integrator output reaches the limit of the acceptable range.

The second scheme involves switching off or resetting the input to the integrator when the control signal for the actuator reaches the saturation value. The scheme is called “Conditional Integration” and requires an additional feedback loop to track the control signal. The third scheme is a classical approach called “Tracking Anti-Windup”. The structure of this approach is quite similar to the second scheme involving another extra feedback loop that will track the output signal. The general idea of this scheme is that it will track the difference between saturated and unsaturated control signal and reduce the input signal to the integrator accordingly.

The two papers mentioned above discuss a software package that has been developed in the SIMULINK/MATLAB environment to investigate the performance of these four different anti-windup implementations for PID controllers. Some simulation results on the capability of each scheme have also been presented and it can be concluded that the limited integrator approach is a satisfactory method, provided the integrator elements of the controller allow implementation of this form of limiting

The final control term is the derivative term. This control action will have no direct influence to the final steady state value of error. However, properly tuned, it can provide rapid correction based on the rate of change of the controlled variable. In many situations the derivative term is omitted because it tends to increase the effect of measurement noise and can thus degrade the overall performance of the controller.

In cases where there is no derivative term the PID controller is reduced to a PI controller having only the proportional and integral terms and thus has only two principal parameters for adjustment. For PID and PI controllers inappropriate tuning of the adjustable parameters can result in instabilities within the controlled process.

Many previous researchers have used the performance of a PI controller as a benchmark against which the performance of other forms of controller for the pH neutralization process can be compared. In this research, the PI controller is again used as a reference against which other forms of control can be compared. This section describes the procedures followed in attempting to tune a PI controller for the pH neutralization pilot plant. Based on the performance of this controller some objectives will be outlined for more advanced types of controller (such as a Fuzzy Logic Controller).

Figure 5:1 shows the MATLAB/SIMULINK representation of the PI controller for the pH neutralization pilot plant. As shown in the figure there are two controller gains; the Proportional Gain and the Integral Gain which represent the first two control terms that have been discussed previously.

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Figure 5:1: MATLAB/Simulink representation for the PI controller

Since the research is not focusing on the investigation of integral windup phenomena, the first anti-windup approach (i.e. the use of Limited Integrators) has been chosen and the other approaches have not been applied. As described above, the use of limited integrators is the simplest approach to overcome the problem of windup and involves setting low and high saturation limits on the integral action.

Thus, when the output reaches either of these the limiting value, the integral action is turned off to prevent integral windup.

As shown in the Figure 5:1 the MATLAB/Simulink environment includes an integrator function which has an option of limiting and allows upper and lower limits to be set by the user. The output of the integrator is determined for three different conditions. The first condition is when the output integral is less than or equal to the Lower saturation limit and the input is negative. For that case the output is held at the Lower saturation limit. The second condition is when the output integral is between the Lower saturation limit and the Upper saturation limit. The output for this situation is simply given by the integral of the input. The third condition is when the integral is greater than or equal to the Upper saturation limit and the input is positive and the output in this case is held at the Upper saturation limit. For this application involving the pH neutralization process pilot plant the limited integrator in the PI controller of Figure 5:1 was set to 0 for the lower limit and 100 for the upper limit.

These values represent the fact that the position of a valve cannot be any more open than fully open (100% opening) and also cannot be driven in a negative direction beyond the fully closed condition (0%valve opening).