Compulsory exercise for Lecture 5
1.
Parameter estimation of a DC motor with least squares (LS) method: This web page presents a DC
motor. The web page includes some experimental data. Estimate K, T and L
using the ordinary least squares method. As known data for the estimation,
use control signal u [V] and speed S [krpm]. Do not use any special function
in Matlab for the LS estimation, i.e., program from scratch the formulas that
calculate the estimate. Finally, check, qualitatively, with a simulation if
the model is good. [Karla]
2.
Parameter estimation of an air heater using the grid optimization
method: This web page
presents an air heater. The web page includes some experimental data. Make a
Matlab program which estimates the heater gain K_h, the time constant
theta_t, the time-delay theta_d, and the environmental temperature T_env with
the grid optimization method. Finally, run a simulation that (hopefully)
demonstrates that the adapted model represents the real air heater well.
(Tip 1: Data can be loaded into the Matlab workspace with the load command.
Tip 2: At each grid point, a simulation is run. Tip 3: A time-delay can be
implementented with an array which contents are moved one array “cell” at
each simulation iteration.) [Aleksander]
3.
Parameter estimation of the air heater using the nonlinear least
squares (NLS) method: As Problem 2, but now use nonlinear least
squares method implemented with fmincon() in Matlab.
(Tip: The objective function is calculated from a simulation of the model. In
other words: At each iteration, the optimizer (fmincon) runs a simulation.) [Duo]
4.
Comparison of estimation results: Which of the grid
method and the NLS method gives the best parameter estimates for the air
heater? (Design the comparison yourself.) [Abhilash]
5.
Subspace identification of the air heater: Try to identify an input/output model (a
discrete-time state space model) of the air heater using subspace
identification (n4sid() in Matlab). Check if the model is good.
(Tip 1: The process contains a time-delay of some seconds. This may cause
problems for the identification with n4sid since the model form assumed by
n4sid does not directly include any time-delay term. Cf. the comments in the
lecture about this.
Tip 2: Matlab
script for subspace identification of DC motor using these experiemental
data, demonstrated in the lecture 18th March 2018.) [Xiaodong]
Comment: Above, there are no exercises about
observers, although this topic was introduced in the lecture Friday 16th
March. Exercises about observers will instead be included in the exercises
for Lecture 6.
Updated 11 April 2018 by Finn Aakre Haugen, course teacher.
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