Fundamentals of Control Theory

According to classic control theory, PID controllers (and their simplified forms) are the most common controller types in industrial environments. Process control with the Levitronix pump controllers is accomplished using a PI controller, which will be described in this topic.

Closed Feedback Control Loops

Feedback loops are characterized by three main elements (as show in Figure 1):

• Controller (in our case the pump controller): receives inputs, computes a response, and operates an actuator to change the performance of a system to obtain a certain output
• System or Plant (in our case the motor and hydraulic loop): composed of all other elements that have an influence on the performance
• Sensor (in most cases a flowmeter or a pressure sensor): evaluates the system output and communicates it to the controller

The working principle is as follows:

1. The user sets the Reference (or setpoint), for example the target flowrate
2. The controller compares the setpoint with the flowmeter measurement
3. Their difference, called Error, is used by the controller to define how to adapt the pump speed
4. The new speed is the Input to the system
5. As s result of the new pump speed, the flowrate changes (system Output)
6. The flowrate is measured again by the flowmeter, and the result is sent as a feedback to the controller to run the subsequent control loop

PID Controllers

If we dive deeper in the PID controller (Figure 2), we can see how the controller responds to the error e(t) to propose a new input to the plant.

• The controller evaluates the entity of the current error, and multiplies it by a constant factor K_p (P gain)
• The controller evaluates the entity of the past error by integrating it over a certain time window. The integral of the error is multiplied by a constant factor K_i (I gain)
• The controller can also try to predict how the error will evolve in the future, by calculating its derivative. The derivative of the error is multiplied by a constant factor K_d (D gain).

Levitronix controllers don’t use the derivative term, and therefore they are PI controllers.

The practical meaning of the P and I terms is that:

• The P term gives a strong response to sudden changes in the setpoint or in the system, since the error suddenly becomes very large. The strength of the response depends on the P gain value. If the gain is too low, the system will react very slowly; if it’s too high the controller will become too reactive and provide an un-necessarily strong response which will cause an overshoot. Since the P term reacts proportionally to the error, this term becomes negligible once the error is sufficiently small. This means that the setpoint might never be reached using this term alone.
• The I term takes care of this shortcoming of the P term. In fact, even a small error (once it’s integrated over a sufficiently long window of time) will cause the controller to build up a reaction. This reaction will (over time) become strong enough to close the gap between setpoint and actual performance value. From this qualitative overview, it can be deducted that this term becomes dominant at the end of the transient.

P and I gains

Levitronix controllers have some default value for the P and I gains. These values are calibrated to provide a moderate response. In fact, a very dynamic response might cause undesired overshoots and anyways, in many application cases, the system is operated at a fixed working point (e.g. in steady flow recirculation systems). For such applications, low PI gains are indicated because there is only one step-response transient in the whole process (the startup of the plant), and therefore a slightly longer transient is acceptable.

In other processes, a dynamic response is key for an optimal production, and therefore the control loop must be tuned to provide an immediate response to setpoint or system changes. Examples of such applications are pulsating flows, and safety pumps used for redundancy.

Since the system (composed of tubes, valves, filters, fluid, etc) is different for every use case, it is impossible to accurately predict what the PI gains should be, and therefore they must be tuned during installation. If tuning is needed, it is important to perform it on the definitive plant (all the right components in place, and with the intended process fluid). Even minor changes in the plant could result in controller reliability issues.