Learn more about the Sensitivity Variable
Professionals who tune PID controllers using manual methods tend to agree that understanding the Process Gain of their system is of the up-most importance. Among industry practitioners the Process Gain is often referred to as the “how far” or even the “sensitivity” variable and yet these descriptions can be rather vague to beginners. So, exactly what is Process Gain and how does it enable safe and effective process control? What is its role in the tuning of PID control loops?
A definition is often a good place to start, and that’s particularly true when trying to understand the role of Process Gain. Process Gain (Kp) is defined as how far the measured Process Variable (PV) moves to a change in Controller Output (CO). The Process Gain is the basis for calculating the Controller Gain (KC) which is the “Proportional” tuning term associated with many of the OEM-specific forms of the PID controller. Before we get too far along, however, let’s break the definition of Process Gain down a bit further.
Essentially Process Gain is one of the model parameters that describes how a process behaves in response to changing dynamics. As mentioned before, the Process Gain details how far the Process Variable moves when the Controller Output changes. When designing a PID controller, it is importance to know how far to move the controller output when the process variable moves away from Set-Point. When calculating the Controller Gain, the inverse of the Process Gain is used in every Proportional Term tuning correlation. Depending on the amount of Error (SP-PV) in the process, the Controller Gain will dictate how much or how little the final control element should adjust as a corrective action. In that regard, the Controller Gain is the sensitivity variable of the PID controller. That’s a critical insight to know when tuning PIDs, and it’s the reason why Process Gain is typically the focal point for most practitioners. It must be able to accommodate subtle changes that result from daily changes in the weather as well as significant changes that stem from disturbances upstream of the process.
While a definition is helpful for some others may benefit from a more practical example. Let’s consider Process Gain in the context of the cruise control function in an automobile. If you’ve ever driven a car then you probably know that cruise control is used to keep the car moving at a constant speed. The rotation of the car’s wheels serves as the measured Process Variable. The accelerator – its angle more specifically – is the device that regulates the flow of fuel into the engine and that functions as the Controller Output. Adjustments are necessary because most roads are not perfectly flat, a headwind creates resistance, etc. Essentially these are disturbances for which cruise control must provide an appropriate correction. It is the value for Process Gain that tells us how sensitive the speed of the car is to gas pedal changes. As you can imagine that value will need to be different when applied to a small sedan versus an oversized truck.
Processes Gain is one of three (3) model parameters that are typically calculated when tuning PID controllers – the others being Process Time Constant (ƮP) and Process Dead-Time (θP). Manual calculation of those parameters can be effective when the associated data is stable. Accurate calculation can quickly become difficult when the trended data is noisy and/or oscillatory. Given the importance of Process Gain and the other two model parameters the use of tuning software can provide meaningful benefits. In particular, software capable of modeling non-steady state data has been shown to provide more accurate model parameters, and it automatically converts model values into the associated tuning coefficients for use with your plant’s PID controller.
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