1. Islamic University of Gaza Faculty of Engineering
Electrical Engineering Department
Control Systems Design, Dr. Moayed Almobaied

2. CH1: Introduction Islamic University of Gaza Faculty of Engineering
Electrical Engineering Department
CH1: Introduction
Control Systems Design, Dr. Moayed Almobaied

3. Islamic University of Gaza Faculty of Engineering
Electrical Engineering Department
Control Systems Design, Dr. Moayed Almobaied

4. System Configurations
Islamic University of Gaza
Faculty of Engineering
Electrical Engineering Department
System Configurations
Open-Loop Systems
Closed-Loop (Feedback Control) Systems
Control Systems Design, Dr. Moayed Almobaied

5. Analysis and Design Objectives
Islamic University of Gaza
Faculty of Engineering
Electrical Engineering Department
Analysis and Design Objectives
Analysis: is the process by which a system’s performance is determined. For example, we evaluate the system transient response and steady-state error to determine if they meet the desired specifications.
Design: is the process by which a system’s performance is created or changed. For example, if a system’s transient response and steady-state error are analyzed and found not to meet the specifications, then we change parameters or add additional components to meet the specifications.
Control Systems Design, Dr. Moayed Almobaied

6. Three major objectives of systems analysis and design:
Islamic University of Gaza
Faculty of Engineering
Electrical Engineering Department
A control system is dynamic: It responds to an input by undergoing a transient response before reaching a steady-state response that generally resembles the input.
Three major objectives of systems analysis and design:
Producing the desired transient response.
Reducing steady-state error.
Achieving stability.
Control Systems Design, Dr. Moayed Almobaied

7. Robust design. (sensitive to parameter changes)
Islamic University of Gaza
Faculty of Engineering
Electrical Engineering Department
Other Considerations
Factors affecting hardware selection, such as motor sizing to fulfill power requirements and choice of sensors for accuracy, must be considered early in the design.
Finances are another consideration. Control system designers cannot create designs without considering their economic impact. Such considerations as budget allocations and competitive pricing must guide the engineer.
Robust design. (sensitive to parameter changes)
Control Systems Design, Dr. Moayed Almobaied

8. The Design Process Islamic University of Gaza Faculty of Engineering
Electrical Engineering Department
The Design Process
Control Systems Design, Dr. Moayed Almobaied

9. Test waveforms used in control systems
Islamic University of Gaza
Faculty of Engineering
Electrical Engineering Department
Test waveforms used in control systems
Control Systems Design, Dr. Moayed Almobaied

10. CH2: Modeling in the Frequency Domain
Islamic University of Gaza
Faculty of Engineering
Electrical Engineering Department
CH2: Modeling in the Frequency Domain
The next step is to develop mathematical models from schematics of physical systems.
We will discuss two methods:
(1) Transfer functions in the frequency domain
(2) State equations in the time domain
Control Systems Design, Dr. Moayed Almobaied

11. Islamic University of Gaza
Faculty of Engineering
Electrical Engineering Department
The first step in developing a mathematical model is to apply the fundamental physical laws of science and engineering.
For example, when we model electrical networks, Ohm’s law and Kirchhoff’s laws, which are basic laws of electric networks, will be applied initially. We will sum voltages in a loop or sum currents at a node.
When we study mechanical systems, we will use Newton’s laws as the fundamental guiding principles. Here we will sum forces or torques.
Control Systems Design, Dr. Moayed Almobaied

12. Islamic University of Gaza
Faculty of Engineering
Electrical Engineering Department
These laws are:
Kirchhoff’s voltage law: The sum of voltages around a closed path equals zero.
Kirchhoff’s current law: The sum of electric currents flowing from a node equals zero.
Newton’s laws: The sum of forces on a body equals zero; the sum of moments on a body equals zero.
Control Systems Design, Dr. Moayed Almobaied

13. Islamic University of Gaza
Faculty of Engineering
Electrical Engineering Department
Kirchhoff’s and Newton’s laws lead to mathematical models that describe the relationship between the input and output of dynamic systems. One such model is the linear, time-invariant differential equation:
Many systems can be approximately described by this equation, which relates the output, c(t), to the input, r(t), by way of the system parameters, di and bj.
Control Systems Design, Dr. Moayed Almobaied

14. Islamic University of Gaza
Faculty of Engineering
Electrical Engineering Department
We would prefer a mathematical representation, where the input, output, and system are distinct and separate parts.
For example, we would like to represent cascaded interconnections, where a mathematical function, called a transfer function, is inside each block, and block functions can easily be combined for ease of analysis and design.
Control Systems Design, Dr. Moayed Almobaied

15. Islamic University of Gaza
Faculty of Engineering
Electrical Engineering Department
Laplace Transform
A system represented by a differential equation is difficult to model as a block diagram. Thus, we now lay the groundwork for the Laplace transform, with which we can represent the input, output, and system as separate entities. Further, their interrelationship will be simply algebraic
(23 March 1749 – 5 March 1827) was a French scholar whose work was important to the development of mathematics, statistics, physics and astronomy
Control Systems Design, Dr. Moayed Almobaied

16. Islamic University of Gaza
Faculty of Engineering
Electrical Engineering Department
Laplace Transform
Thus, knowing f(t) and that the integral exists, we can find a function, F(s), that is called the Laplace transform of f(t).
Control Systems Design, Dr. Moayed Almobaied

17. Islamic University of Gaza Faculty of Engineering
Electrical Engineering Department
Control Systems Design, Dr. Moayed Almobaied

18. Inverse Laplace transform
Islamic University of Gaza
Faculty of Engineering
Electrical Engineering Department
Inverse Laplace transform
The inverse Laplace transform allows us to find f(t) given F(s)
Control Systems Design, Dr. Moayed Almobaied

19. Islamic University of Gaza Faculty of Engineering
Electrical Engineering Department
Control Systems Design, Dr. Moayed Almobaied

20. Islamic University of Gaza Faculty of Engineering
Electrical Engineering Department
Control Systems Design, Dr. Moayed Almobaied

21. Partial-Fraction Expansion
Islamic University of Gaza
Faculty of Engineering
Electrical Engineering Department
Partial-Fraction Expansion
To find the inverse Laplace transform of a complicated function, we can convert the function to a sum of simpler terms for which we know the Laplace transform of each term. The result is called a partial-fraction expansion.
Control Systems Design, Dr. Moayed Almobaied

22. Partial-Fraction Expansion
Islamic University of Gaza
Faculty of Engineering
Electrical Engineering Department
Partial-Fraction Expansion
If F1(S)=N(S)/D(S) where the order of N(s) is less than the order of D(s), then a partial-fraction expansion can be made.
If the order of N(s) is greater than or equal to the order of D(s), then N(s) must be divided by D(s) successively until the result has a remainder whose numerator is of order less than its denominator.
Control Systems Design, Dr. Moayed Almobaied

23. Case 1. Roots of the Denominator of F(s) Are Real and Distinct
Islamic University of Gaza
Faculty of Engineering
Electrical Engineering Department
Case 1. Roots of the Denominator of F(s) Are Real and Distinct
Case 2. Roots of the Denominator of F(s) Are Real and Repeated
Case 3. Roots of the Denominator of F(s) Are Complex or Imaginary
Control Systems Design, Dr. Moayed Almobaied

24. The Transfer Function Islamic University of Gaza
Faculty of Engineering
Electrical Engineering Department
The Transfer Function
Control Systems Design, Dr. Moayed Almobaied

25. This equation is a purely algebraic expression.
Islamic University of Gaza
Faculty of Engineering
Electrical Engineering Department
This equation is a purely algebraic expression.
If we assume that all initial conditions are zero:
Control Systems Design, Dr. Moayed Almobaied

26. Islamic University of Gaza Faculty of Engineering
Electrical Engineering Department
Control Systems Design, Dr. Moayed Almobaied

27. Islamic University of Gaza Faculty of Engineering
Electrical Engineering Department
Control Systems Design, Dr. Moayed Almobaied

28. Islamic University of Gaza Faculty of Engineering
Electrical Engineering Department
Control Systems Design, Dr. Moayed Almobaied

29. Islamic University of Gaza
Faculty of Engineering
Electrical Engineering Department
Let us now develop a technique for simplifying the solution for future problems.
Take the Laplace transform of the equations in the voltage-current column assuming zero initial conditions.
Control Systems Design, Dr. Moayed Almobaied

30. Operational Amplifiers
Islamic University of Gaza
Faculty of Engineering
Electrical Engineering Department
Operational Amplifiers
Control Systems Design, Dr. Moayed Almobaied

31. Inverting Operational Amplifier
Islamic University of Gaza
Faculty of Engineering
Electrical Engineering Department
Inverting Operational Amplifier
Control Systems Design, Dr. Moayed Almobaied

32. Noninverting Operational Amplifier
Islamic University of Gaza
Faculty of Engineering
Electrical Engineering Department
Noninverting Operational Amplifier
Control Systems Design, Dr. Moayed Almobaied

33. Translational Mechanical System Transfer Functions
Islamic University of Gaza
Faculty of Engineering
Electrical Engineering Department
Translational Mechanical System Transfer Functions
Control Systems Design, Dr. Moayed Almobaied

34. Islamic University of Gaza Faculty of Engineering
Electrical Engineering Department
Control Systems Design, Dr. Moayed Almobaied

35. Islamic University of Gaza Faculty of Engineering
Electrical Engineering Department
Control Systems Design, Dr. Moayed Almobaied

36. for the spring Islamic University of Gaza Faculty of Engineering
Electrical Engineering Department
for the spring
Control Systems Design, Dr. Moayed Almobaied

37. Rotational Mechanical System Transfer Functions
Islamic University of Gaza
Faculty of Engineering
Electrical Engineering Department
Rotational Mechanical System Transfer Functions
Control Systems Design, Dr. Moayed Almobaied

38. Transfer Functions for Systems with Gears
Islamic University of Gaza
Faculty of Engineering
Electrical Engineering Department
Transfer Functions for Systems with Gears
Control Systems Design, Dr. Moayed Almobaied

39. Electromechanical System Transfer Functions
Islamic University of Gaza
Faculty of Engineering
Electrical Engineering Department
Electromechanical System Transfer Functions
Control Systems Design, Dr. Moayed Almobaied

40. End of Lecture 3 H.W : 11/2/2018 Ch2:8,18,21,23,26
Islamic University of Gaza
Faculty of Engineering
Electrical Engineering Department
End of Lecture 3
H.W : 11/2/2018
Ch2:8,18,21,23,26
Control Systems Design, Dr. Moayed Almobaied