When operating in a disturbance-free environment, the nominal input of value 50 keeps
the plant along its constant trajectory of value 2000. Any disturbances would cause the
plant to deviate from this value. The PID Controller’s task is to add a small correction to
the input signal that brings the system back to its nominal value in a reasonable amount
of time. The PID Controller thus needs to work only on the linear deviation dynamics even
though the actual plant itself might be nonlinear. Thus, you might be able to achieve
effective control over a nonlinear system in some regimes by designing a PID controller
for a linear approximation of the system at equilibrium conditions.
Linear Process Models
A common use case is designing PID controllers for the steady-state operation of
manufacturing plants. In these plants, a model relating the effect of a measurable input
variable on an output quantity is often required in the form of a SISO plant. The overall
system may be MIMO in nature, but the experimentation or simulation is carried out in a
way that makes it possible to measure the incremental effect of one input variable on a
selected output. The data can be quite noisy, but since the expectation is to control only
the dominant dynamics, a low-order plant model often suffices. Such a proxy is obtained
by collecting or simulating input-output data and deriving a process model (low order
transfer function with unknown delay) from it. The excitation signal for deriving the data
can often be a simple bump in the value of the selected input variable.
Advanced System Identification Tasks
In PID Tuner, you can only identify single-input, single output, continuous-time plant
models. Additionally, PID Tuner cannot perform the following system identification tasks:
- Identify transfer functions of arbitrary number of poles and zeros. (PID Tuner can
identify transfer functions up to three poles and one zero, plus an integrator and a
time delay. PID Tuner can identify state-space models of arbitrary order.) - Estimate the disturbance component of a model, which can be useful for separating
measured dynamics from noise dynamics. - Validate estimation by comparing the plant response against an independent dataset.
- Perform residual analysis.
If you need these enhanced identification features, import your data into the System
Identification app (System Identification). Use the System Identification app to
perform model identification and export the identified model to the MATLAB workspace.
Then import the identified model into PID Tuner for PID controller design.
System Identification for PID Control