Closed-loop identification using quantized data
A model of a system is important for applications such as simulation, prediction and control.
Closed-loop identification (CLIO) is a means of identifying a process model while the process
is still under feedback control. The motivation of this project is to find a way to do closed-loop
identification while causing minimum disruption to the controlled process.
There are two main categories of closed loop identification. One is closed-loop identification
with external excitation (Ljung 1987, System Identification: theory for the user, Englewood
Cliffs, NJ: Prentice-Hall). Another is relay identification (A strom and Hagglund I984a, Automatic
Tuning of Simple Regulators with Specifications on Phase and Amplitude Margins,
Alltomatim, Vo1.20, No.5. pp645-651 ). The first achievement of this thesis is the establishment
of a connection between previously unrelated facts by comparing the two main categories of
closed loop identification methods. Their advantages and disadvantages were highlighted
through case studies.
The second. and the main achievement of this thesis is to propose a new closed-loop identification
scheme for a single-input-single-output (5IS0) control loop. It is based on a quantizer insel1ed
into the feedback path. The novel contribution of this thesis is to bring the closed-loop
identitication with external excitatiun method and the relay identification method into a unified
framework for the first time. It gives recommendations about the appropriate method to use for
a given quantizer interval. When the quantization interval is small, the quantization error is persistently
exciting, equivalent to an external excitation. The two-stage (step) method can be applied.
When the quantization interval is large. the relay method can be applied instead. Nonlinearity
caused by the quantizer is analyzed. which indicates that nonlinearity increases with the
quantization interval. Simulations and experiments showed that the proposed closed-loop idclItification
schemc based on quantization is successful.
The third achievement of this thesis is the implementation. testing and extension of a quantized
regression (QR) algorithm that retrieves the underlying information from quantized signals
such as those from the analogue to digital converter of a plant instrument. The algorithm is a
combination of the 'Gaussian Fit' schcme with expectation-maximization (EM) algorithm. The
new QR algorithm can optimally estimate the model parametcrs and recover the underlying
signal at the same time for an arbitrary number of quantizer levels.