electronic and communication engineering technology

51.1 The definition of the control and automatic control system ...51.2 The structure of a typical automatic control system ...71.3 Difference between closed-loop and open-loop system ..

HO CHI MINH CITY UNIVERSITY OF TECHNOLOGY AND EDUCATION FACULTY FOR HIGH QUALITY TRAINING

FINAL PROJECT

AUTOMATIC CONTROL SYSTEMS

LƯƠNG NGỌC PHƯƠNG QUỲNH

Advisor: VŨ VĂN PHONG, PhD.

Ho Chi Minh City, June 2022

HO CHI MINH CITY UNIVERSITY OF TECHNOLOGY AND EDUCATION FACULTY FOR HIGH QUALITY TRAINING

Advisor: VŨ VĂN PHONG, PhD.

Ho Chi Minh City, June 2022

Table of Contents

TASK 1: Basic concepts of the Automatic Control System 5

1.1 The definition of the control and automatic control system 5

1.2 The structure of a typical automatic control system 7

1.3 Difference between closed-loop and open-loop system 9

1.4 Consider the liquid-level control system in Fig.5, please list the components of this system and make block diagram of this system This system is open-loop or closed-loop system? 11

TASK 2: Mathematical Model 11

2.1 Block Diagram 11

2.2Using Matlab to find the closed-loop transfer function 12

2.3 State-space equation 14

TASK 3: Transient Response and stability Analysis 17

3.1 Analyse the behaviour and response of the first-order system as follow: 17

3.2 Consider the Hubbe Space Telescope is modelled in Fig.8 Analyse the behavior and response of this system .18

3.3 Taken into account the following system 20

3.4 Consider the Disk Drive Read System in Figure 9 22

TASK 4: PID Controller Design 25

4.1 Please explain 25

4.2 Let us consider the following system 31

4.3 Consider a system in the following figure 39

4.4 The DC Motor in Fig.31 is modelled in the following transfer function 42

Reference 45

Table of Figure and Table

Figure 1 Figure of Task 1 5

Figure 2 A control system 5

Figure 3 Automobile interior cabin temperature control system 7

Figure 4 The structure of automatic control system 7

Figure 5 11

Figure 6 Block Digram of system Fig 5 11

Figure 7 Structure of Pneumatic System 12

Figure 8 Block diagram of Pneumatic system 12

Figure 9 13

Figure 10 Using Matlab to determine the transfer function 13

Figure 11 Enter Transfer funtion into Matlab 14

Figure 12 Mechanical system 14

Figure 13 Simulate System with Simulink 15

Figure 14 Simulate System with Simulink 15

Figure 15 The Waveform in Simulink 16

Figure 16 Simulate with Simulink 17

Figure 17 Simulate the system in Matlab with unity step signal 18

Figure 18 Block diagram of the system 20

Figure 19 21

Figure 20 Plot the poles and zeros 21

Figure 21 22

Figure 22 22

Figure 23 The mathematical form of PID algorithm 26

Figure 24 P-control behavior is mathematically illustrated 27

Figure 25 P-controller output for step input 28

Figure 26 I-control behavior is mathematically illustrated 29

Figure 27 I-controller output for step input .30

Figure 28 D-control behavior is mathematically illustrated 30

Figure 29 D-controller output for step input 31

Figure 30 Blcok Diagram of this system 31

Figure 32 Block Diagram of the system 39

Figure 31 Model of the DC Motor with the inertial load 42

Table 1 Comparison chart 10

TASK 1: Basic concepts of the Automatic Control System

Figure 1 Figure of Task 1

Before studying the automatic control system, there are several concepts of control filed that need to understand clearly The requirements for this task are that students have to answer the following questions:

1.1 The definition of the control and automatic control system

Please provide the definition of the control and automatic control; and give a real specific example of automatic control.

What is a control system?

A control system is a system capable of monitoring and regulating the operation of a process or a plant The study of control system is essentially a study of an important aspect of systems engineering and its applications A control system consists of subsystems and processes (or plants) assembled for the purpose of controlling the outputs of the process For example, a furnace produces heat as a result of the flow of fuel In this process, flow of fuel in the input, and heat to be controlled is the output.

Figure 2 A control system

There are two common classes of control systems, with many variations and combinations: logic or sequential controls, and feedback or linear controls There is also

Float

fuzzy logic, which attempts to combine some of the design simplicity of logic with the utility of linear control Some devices or systems are inherently not controllable.

What is a automatic control system?

In a manual control system a machine will be operated by a person but in the case of an automatic control system machine will do the operation automatically The automatic control system has a controller so it can perform the operation on its own Basically, the control system is a combination of elements and subsystem which needs to maintain a quantity The control system can maintain a process with the help of feedback control, this would help to maintain the specific variables close to the required values So the control system can meet the requirement of the process by adjusting the selected variables in the system The feedback control can make use of an output of the system to influence the input of the same system The automatic control system would have electronic equipment and it uses current and voltage to communicate Control will be implemented in the sensors, valves, and other equipment in the process.

The automatic control system will use, for the regulation and quality control of processes and the environment The control system is used in many industrial processes, a process is a device, plant, or system which is under control The process control is done by a control system, the control system would convert the variable to the required variable There are manual and automatic control systems if a human operator is required to give input throughout the process then it is manual control In an automatic control system, there will be a controller which can replace the human operator and this will be very useful and this controller is set to control the process accurately In most cases, the function of the control system is to control the physical variables such as temperature, voltage, frequency, flow rate, current, position, speed, etc, and all these are called the controlled variables[1].

Example: Automobile interior cabin temperature control system

Many luxury automobiles have thermostatically controlled air-conditioning systems for the comfort of the passengers Sketch a block diagram of an air-conditioning system where the driver sets the desired interior temperature on a dashboard panel Identify the funtion of each element of the thermostatically controlled cooling system[2].

Figure 3 Automobile interior cabin temperature control system 1.2 The structure of a typical automatic control system

Please describe the structure of a typical automatic control system Please list the typical components and their function?

The structure of a typical automatic control system include block controller, sensor, actor, and plant

Figure 4 The structure of automatic control system

In the controlled behaviour approach the model describes the behaviour of the plant and the controller joined together For the implementation the control algorithm has to be extracted from the combined model.

The logic controller approach tries to define the inputoutput behaviour of the controller, which satisfies all the system requirements Using this method the control program can be deduced directly from the obtained I/Obehaviour This approach leads to the physical implementation of the control program, but simulation is required to validate the closed-loop behaviour.

The control theoretic approach has been investigated by numerous research teams and is getting more and more popular The approach adopts the controller synthesis paradigm from control theory for continuous systems A decomposition of an automation system leads to a structure very similar to a control loop in control engineering (Fig 4) The approach is based on separate models of plant and controller[3].

The typical components and their function?

Automatic control systems may be classified as servo-mechanisms, process control systems and regulators, but whatever the classification be, the same principles of operation are common to them all Every ACS should contain five main components They are: a driver or reference input, an error detector, control elements, a controlled quantity and feedback path elements The basic control system operation may be described by the simple block diagram[4]:

The reference input or driver sets the desired level or position of controlled quantity C in this system The controlled quantity C is the resulting level or position of variable parameter, which is the position to be controlled by this ACS The feedback path elements H supply a feedback signal B that indicates the level of the controlled quantity C The error detector receives the feedback signal B and compares it with the input command signal R; any error (or difference between B and R) produces an output or

resulting signal E Control elements G receive, amplify and transform the output signal E to maintain the controlled quantity at the desires level[4].

1.3 Difference between closed-loop and open-loop system

Basis For Comparison

Open Loop System Closed Loop System

Definition The system whose control action is free from the output is known as the open loop control system.

In closed loop, the output depends on the control action of the Construction Simple Complex Reliability Non-reliable Reliable Accuracy Depends on

Accurate because of feedback.

Stability Stable Less Stable Optimization Not-Possible Possible

Calibration Difficult Easy System

Affected Not-affected

Linearity Non-linear Linear Examples Traffic light, system, speed and pressure control system, refrigerator, toaster.

Table 1 Comparison chart Example for Open Loop Control System:

The automatic washing machine is the example of the open loop system The operator manually sets the operating time of the machine The machine stops operating after the set time, even the desire cleanliness of clothes are not obtained This happens because the machine has no feedback system which signals the control action of the system for desired output.

Example for Closed Loop Control System:

Suppose in the above example of closed dryer we are using the transducer which senses the dryness of the clothes and provides the feedback signal to the controller relating to dryness Here the dryness is the output of the system The sensor act as a feedback of the system The sensor gives the signal to the controller of the machine, and hence the dryer provides the desired output.

Figure 17 Simulate the system in Matlab with unity step signal 3.2 Consider the Hubbe Space Telescope is modelled in Fig.8 Analyse the behavior and response of this system.

Fig 8: The block-diagram of the system

Ignore the effect of disturbance, please determine the transfer function between Y(s) and R(s).

3.3 Taken into account the following system

Figure 18 Block diagram of the system • Find the poles and zeros of the closed-loop system in Figure 18

Figure 19

Figure 20 Plot the poles and zeros

• Based on the position of poles on complex plane, please check the stability of the system.

Because the poles of the transfer function are all to the left of the complex plane ( s = -2; -0.5 +1.323j; -0.5-1.232j)

→ the transfer function is stable.

• Simulate the system with unity step input by Matlab/Simulink Comment the obtained results.

Figure 21

Figure 22

→ The transfer function is stable, according to the results Although it will take a long time to stabilize (it takes up to 15 seconds for the transfer function to become stable).

3.4 Consider the Disk Drive Read System in Figure 9.

Fig 9: Disk drive read system

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• Please determine conditions of parameters of P controller such that the system is stable according to the Routh-Hurwirtz criterion.

• Select two values of Kp, one satisfies the Routh-Hurwirtz condion and another is not, then using Matlab to simulate above system with two valules of Kp The input signal is unitiy step input signal Based on the obtained the simulation results, please evaluate the stability of the system with P controller when the parameter of P controller is determined based on the Routh-Hurwirtz criterion.

Choose Kp = 20 and Kp = 100

+ Kp = 20

+ Kp = 100

→ Evaluate the stability of the system with P controller:According to Routh-Hurwitz criterion for the system to be stable, K must be less than 84 and greater than 0 We discover that the system is unstable when K is bigger than 84 (exactly equal to 100) As a result, the PID controller is very important balancing the stable system.

TASK 4: PID Controller Design 4.1 Please explain

What is the PID controller?

A proportional–integral–derivative controller (PID controller or three-term controller) is a control loop mechanism employing feedback that is widely used in industrial control systems and a variety of other applications requiring continuously modulated control A PID controller continuously calculates an error value e(t) as the difference between a desired setpoint (SP) and a measured process variable (PV) and applies a correction based on proportional, integral, and derivative terms (denoted P, I, and D respectively), hence the name.

It is important to note that cost benefit ratio obtained through the PID controller is difficult to achieve by other controllers It is found that 97% of the regulatory controllers in industry use PID algorithm The PID controller is popularly known as three term controller- the Proportional (P), Integral (I) and Derivative (D) The desired closed-loop system performance can be achieved with an appropriate adjustment of controller settings This procedure is known as controller tuning Hundreds of tools, methods and theories

are available for tuning the PID controller However, finding optimal parameters for the PID controller is still a tricky task, in practice still the trial and error method is used for tuning process by the control engineers The controller can provide optimized control action, and minimized error performance with optimum tuning of the three parameters in the PID controller algorithm The mathematical form of PID algorithm is represented in Fig.23 [5].

Figure 23 The mathematical form of PID algorithm

In practical terms, PID automatically applies an accurate and responsive correction to a control function An everyday example is the cruise control on a car, where ascending a hill would lower speed if constant engine power were applied The controller's PID algorithm restores the measured speed to the desired speed with minimal delay and overshoot by increasing the power output of the engine in a controlled manner.

The roles of the P, I, D of PID control in the control system Proportional (P) Control:

One type of action used in PID controllers is the proportional control Proportional control is a form of feedback control It is the simplest form of continuous control that can be used in a closed-looped system P-only control minimizes the fluctuation in the process variable, but it does not always bring the system to the desired set point It provides a faster response than most other controllers, initially allowing the P-only controller to respond a few seconds faster However, as the system becomes more complex (i.e more complex algorithm) the response time difference could accumulate, allowing the controller to possibly respond even a few minutes faster Although the P-only controller does offer the advantage of faster response time, it produces deviation from the set point This deviation is known as the offset, and it is usually not desired in a process The existence of an offset implies that the system could not be maintained at the desired set point at steady state It is analogous to the systematic error in a calibration curve, where there is always a set, constant error that prevents the line from crossing the origin The offset can be minimized by combining P-only control with another form of control, such as I- or D- control It is important to note, however, that it is impossible to