ELEC4632 Computer Control Systems

Name of this Assignment Item: Lab Project

Abstract

This report documents a series of experiments conducted to identify, design, and implement control systems for a water-tank (W-T) setup. Beginning with system identification using the linear least squares method, each subsequent lab builds upon the knowledge gained to explore advanced control strategies. Experiments include designing and simulating deadbeat and proportional-integral (PI) controllers, and their real-time implementation on the W-T system.

The results show that while deadbeat control offers faster responses, it often exceeds voltage constraints, making it unsuitable for practical use. Conversely, PI control demonstrates stable real-time performance despite initial discrepancies, successfully regulating the W-T system. Overall, the experiments validate the use of mathematical modeling and control design in real-time applications, providing insights into system dynamics and control strategies.

Lab1

Aim:

The aim of this experiment is to apply the linear least squares method to identify a second-order discrete-time dynamic model for a physical system based on input and output data.

In this experiment, offset compensation was performed to eliminate constant shifts in the input and output signals, ensuring accurate system identification. For the input signal uact the first value was treated as the offset and subtracted from the entire signal to obtain the offset-free input (u). For the output signal yact, the offset was estimated as the mean of the initial steady segment before any input changes. This value was subtracted to generate the offset-free output (y). Removing these offsets ensures that the processed signals start from zero, avoiding bias in parameter estimation and improving the quality of the identified model.

Result:

Prelab

Plotting of offset-free output, input

Simulation and actual output

Comment: The actual output takes longer to stabilize due to potential sensor errors or water level fluctuations, but the small error indicates the model effectively captures system dynamics. While the settling time differs, the model is adequate for system identification, with potential improvements possible through better sensors or nonlinear modeling.

Post lab

Comment: The graph shows that the second-order model fits the actual output more accurately, with a lower MSE (0.0030154) compared to the first-order model. The second-order model captures rapid changes and dynamics better, making it more suitable for system identification.

Lab2

Aim

The aim of this lab is to identify a linear second-order discrete-time model for a water-tank system by collecting and analyzing real-time input-output data using MATLAB and the Simulink Desktop Real-Time Toolbox. Through this process, you will explore the operation of the water-tank system within its linear range, apply the linear least squares method to the experimental data, and deepen your understanding of system behavior. and modeling techniques.

Requirements

Vmin=2.0v                 Water level min = 94

Vmax=3.0v                Water level max = 249

Then calculate the u_offset = 2.5v

Repeating Sequence Stair block should be chosen based on the linear input voltage.

Real-time input-output data collection.

Result:

Raw data

Comment: Because the tank is unstable, our data is not smooth at each periods. So we cut off the data from 800.25.

Plotting of non-offset free input, output

Simulation and actual result

Lab3

Aim

The purpose of this laboratory is to identify the W-T system model and design a control system and simulate it using MATLAB and Simulink. Final implementation of state feedback control with observer for both regulation and set point control (Output feedback control)

Methods:

The first part is to simulate two closed-loop control systems according to the experimental steps. Finally, the output (initial condition response) and control input are plotted. The first part is to simulate two closed-loop control systems according to the experimental steps. Finally, the output (initial condition response) and control input are plotted. The goal of setpoint control is to design a control system that outputs some specific constant reference output values as follows The following flow chart shows the state feedback method.

Then the figure shows the block diagram of the output feedback control system with observer.

This function is implemented using Simulink. The Simulink simulation model is shown in the following figure.

Results:

The following figure shows the deadbeat control and non-deadbeat control.

It can be clearly seen that deadbeat control is faster than the non-deadbeat control. But it also has some problem. That is, the deadbeat control input will rapidly rise in a very short period. That may cause dangerous. Thus, in this lab 3 non-deadbeat control will be used.

The following figure shows the compare reference output and Simulink output. Also, the Simulink control input is shown too.

It can be observed that the trajectory of the analogy output is basically the same as that of the tracking reference, and it also coincides in many times.

The maximum and minimum values of Simulink control input are maximum in the first cycle. In the next few cycles, the maximum and minimum values are decreasing. The control input is kept within -0.5 and 0.5. Thus, the design is successfully.

Then use the Simulink model to check the state estimation error. The following figure shows this part.

The initial conditions of the observer and the system are different, but they are equal after the first sampling. Therefore, the functional design of the observer is very accurate.

Lab4

Aim:

This experiment aims to implement and evaluate the real-time performance of the deadbeat output feedback control system from Experiment 3 on the actual w-t system. It includes repeating the system identification from Lab 2 and performing the real-time control system implementation.

Result：

non-offset free output and input

offset free output and input

the 2nd half and entire offset free verification

the deadbeat control compares with non-deadbeat control

Comment: Similar to Lab 3, while deadbeat control provides a faster response, its input voltage exceeds the allowable range of [-0.5, 0.5], requiring us to exclude it from further design considerations.

Set-point control response

Set-point control response with observer and non-zero initial conditions

simulated and actual output feedback control

As can be seen from the figure, the output feedback control function operates normally. The paths of actual output and Simulink output are basically the same. But at the same time, we can see that in the second figure, the actual control input and Simulink control input cannot be the same size. Add 2 to the value of Simulink, and the two images will increase together. No solution has been found after troubleshooting.