How can you compensate for dead time in a PID controller?

1 Use a Smith Predictor

One of the most popular methods of compensating for dead time is using a Smith predictor, which is a feedforward control scheme that adds a model of the process and the dead time to the feedback loop. The idea is to use the model to predict the future output of the process and compare it with the setpoint, instead of using the delayed output. This way, the controller can act on the predicted error, rather than the actual error, and reduce the effect of dead time. However, the Smith predictor requires an accurate model of the process and the dead time, which can be difficult to obtain or maintain in some cases. Moreover, the Smith predictor can be sensitive to disturbances and parameter variations in the process.

2 Use a Pade Approximation

Another method of compensating for dead time is using a Pade approximation, which is a mathematical technique that approximates the dead time by a rational function of a complex variable. The Pade approximation can be used to transform the dead time into a series of poles and zeros in the Laplace domain, which can then be used to design a PID controller using standard methods. The advantage of this method is that it does not require a model of the process, only the dead time. However, the Pade approximation introduces some error and complexity in the controller design, especially for large dead times. Moreover, the Pade approximation can also be sensitive to disturbances and parameter variations in the process.

3 Use a Dahlin Controller

A third method of compensating for dead time is using a Dahlin controller, which is a discrete-time controller that incorporates the dead time into the control algorithm. The Dahlin controller uses a recursive formula to calculate the optimal control action based on the current and past errors, the process gain, and the dead time. The Dahlin controller can achieve good performance and stability for a wide range of processes with dead time, without requiring a model of the process. However, the Dahlin controller requires the knowledge of the process gain and the dead time, which can be hard to measure or estimate in some cases. Moreover, the Dahlin controller can have some limitations in handling nonlinearities and disturbances in the process.

4 Use a Modified PID Controller

A fourth method of compensating for dead time is using a modified PID controller, which is a variation of the standard PID controller that includes some additional terms or parameters to account for the dead time. For example, some modified PID controllers use a filter or a phase lead compensator to improve the phase margin and stability of the system. Other modified PID controllers use a dead time compensator or a setpoint predictor to reduce the overshoot and settling time of the system. The modified PID controllers can be easier to implement and tune than the other methods, as they do not require a model of the process or the dead time. However, the modified PID controllers can have some trade-offs in terms of performance and robustness, depending on the type and magnitude of the dead time and the process dynamics.

5 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?