  We compare the performance of proportional-integral-derivative (PID) control,
linear model predictive control (LMPC), and nonlinear model predictive control
(NMPC) for a physical setup of the quadruple tank system (QTS). We estimate the
parameters in a continuous-discrete time stochastic nonlinear model for the QTS
using a prediction-error-method based on the measured process data and a
maximum likelihood (ML) criterion. In the NMPC algorithm, we use this
identified continuous-discrete time stochastic nonlinear model. The LMPC
algorithm is based on a linearization of this nonlinear model. We tune the PID
controller using Skogestad's IMC tuning rules using a transfer function
representation of the linearized model. Norms of the observed tracking errors
and the rate of change of the manipulated variables are used to compare the
performance of the control algorithms. The LMPC and NMPC perform better than
the PID controller for a predefined time-varying setpoint trajectory. The LMPC
and NMPC algorithms have similar performance.
