Closed-loop identification with external excitation using a quantizer

For the demonstration o f closed-loop identification with external excitation using a quantizer in the temperature loop of the simulation model, the scheme is shown in Figure 5-

10.

In the block diagram, a is white noise with variance 0.25. Quantization error d = y ^ - y is the exciting signal generated by the quantizer, which is persistently exciting. At this moment, the quantizer works as a mid-step quantizer. The two-stage method (Van den H of and Schrama, 1993) was used for identification. The first stage is to identify the sensitivity function with exciting signal d and process input m . In the second stage, the process is identified with simulated input and process output y where simulated input is obtained from exciting signal d and the estimated sensitivity function.

Process

F igure 5-10 Simulation fo r the CLID with a quantizer fo r temperature loop with Van den H o f and Schrama (1993) method.

The standard deviation of the process output is (J^ =0.55 when the quantization interval is 0.005. The standard deviation of the process output in m inimum variance ( 7 is 0.52 by calculation. Three cases were designed in which the quantization intervals are different (as shown in Table 5.3). The identification results are presented in subsection 6.3.2.

Case 1 Case 2 Case 3

Quantization interval (qi) 0.61 0.81 1.05

Equivalent to (7y 1.10 1.47 1.9

T ab e 5.3 CLID with a quantizer simulation conditions fo r pilot plant model simulation

5.6.4 Relay-based identification with a quantizer

The simulation in this subsection demonstrates the relay-based identification using a quantizer in the temperature loop of the simulation model. The identification scheme is shown in Figure 5-11.

In the block diagram, a is white noise with variance 0.25, which is implemented by the band-limited white noise module in Matlab/Simulink. In this work, the quantizer works as a mid-rise quantizer. Only two quantization levels can be used during the identification. The FFT-based method (Wang et al, 1997b) was used for identification. The quantizer output (instead o f the process input m ) is viewed as the input. The output o f the low-pass Butter worth filter y j- (instead of the process input y ) is viewed as the output. The dynamics of the controller and the filter are removed from the identified results by complex dividing.

The standard deviation o f the process output is o ^ = 0.55 when the quantization interval is 0.005. According to the CLPA theory, the standard deviation o f minimum variance for the process output is = 0.52. By the suggestions in Chapter 4, quantization interval equivalent to 4 <7^ is used.

Process

Lowpass Filter

Figure 5-11 Simulation fo r relay based identification with a quantization fo r temperature loop (Wang et al. 1997b).

5 .7 E x p e rim e n ta l eva lu a tio n

The pilot plant itself has been introduced in subsection 5.6.1. The purpose of this section is to describe the various experiments for demonstrating the method of CLED with a quantizer with a real life pilot plant.

5.7.1 Open loop test

In order to test the dynamics of the temperature loop in pilot p la n t, two test signals were used respectively, the random binary signal (RBS) and the step. The test signal was applied at the steam valve and the output is measured from the temperature sensor in the outlet pipe of the tank. In the first test, the test signal is RBS with frequency band from 0 to 1 (i.e. 0 to 1.57 rad/sec since the sampling time used is 4 second) and the amplitude from -0.6m A to 0.6mA. The RBS signal is also generated by function in System Identification Toolbox in Matlab. The input is a unit amplitude step from 12.57 to 13.57 in the second test. Two similar step tests have been done. The open loop identification results are shown in subsection 6.4.1.

5.7.2 Closed-loop identification with external excitation using a quantizer

The level o f the tank was always controlled to be 12mA on a 4-20 mA scale (that is in the middle o f the tank) during the experiment. The cold water inflow and the hot water outflow were always under balance when steady-state was reached. The manipulated variable was the steam flow. The controlled variable was the hot water temperature. A well-tuned PI controller in continuous form was applied (as shown in Figure 5-12, which is the same as Figure 5-10). The setpoint for the temperature loop is 10.5 mA (that is 41.5°C).

Process

F igure 5-12 Experimentation f o r CLID with a quantizer fo r temperature loop

Case 1 hybrid experiment

The reason why case 1 is named ‘hybrid experiment’ is that the process is the real life tank and the computer generated the disturbance a (i.e. by M atlab function). In Figure 5-12, a is white noise with variance 0.25. Quantization error d = — y is viewed as the exciting signal generated by the quantizer. The quantizer works as a mid-step quantizer. The two- stage method (Van den H of and Schrama, 1993) was used for identification.

The open loop identification result conducted with RBS in subsection 5.7.1 can be viewed as the true process. Then the proposed new scheme is conducted in the following steps: • The process is run as normal (with quantization interval very small, for example 0.005,

equivalent to 12 bit A/D). The standard deviation of process output is calculated to be 0.55.

• A specific quantization interval q i= l.l is chosen, i.e. 2 times (7y. The process is run with this quantization interval. The quantizer error excitation y^ - y can be guaranteed to be sufficiently good to do identification. The signal-to-noise ratio is 0.39.