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+++ title = "Bumpless Transfer" author = ["Dehaeze Thomas"] draft = false category = "Control Theory" subcategory = "Fundamentals" +++
- Tags
- [Anti-Windup Control]({{< relref "anti_windup_control.md" >}})
Bumpless transfer consists in switching between two controllers without creating a discontinuity (a "bump") in the control signal \(u\).
A bump occurs because the inactive controller has internal states (integrators, filters) that are not consistent with the signal currently applied to the plant. At the switch, its output differs from the active one, and \(u\) jumps.
The principle is to keep the inactive controller "warm": its states must be consistent with the applied signal \(u_a\) before the switch. Anti-windup is a special case of this, with \(u_a = \text{sat}(u)\).
An example of bumpless transfer between manual and PID control is provided by MathWorks: Bumpless Control Transfer Between Manual and PID Control.
Controllers with an explicit integrator (PID)
The integrator of the offline controller is driven to track the applied signal using back-calculation:
\begin{equation} \dot{x}_i = K_i e + \frac{1}{T_t} \left( u_a - u \right) \end{equation}
This requires the integrator to be explicit, which is one of the reasons why PID controllers are convenient. If the PID is the last element of the chain, its output is \(u\) and the tracking is exact.
Controllers made of biquads
Filters without integrator (notch, low-pass, lead, lag) have fast dynamics and do not need any tracking. The offline chain is simply run in parallel, fed with the same error signal \(e\), and its states converge by themselves.