Islamic University of Gaza Faculty of Engineering Electrical

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

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

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

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

Islamic University of Gaza Faculty of Engineering Electrical Engineering Department Analysis and Design Objectives Ø 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. Ø 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 additional components to meet the specifications. Control Systems Design, Dr. Moayed Almobaied

Islamic University of Gaza Faculty of Engineering Electrical Engineering Department Ø 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. Ø o o o 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

Islamic University of Gaza Faculty of Engineering Electrical Engineering Department Other Considerations Ø 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. Ø 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. Ø Robust design. (sensitive to parameter changes) Control Systems Design, Dr. Moayed Almobaied

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

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

Islamic University of Gaza Faculty of Engineering Electrical Engineering Department CH 2: 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

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. Ø 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. Ø 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

Islamic University of Gaza Faculty of Engineering Electrical Engineering Department These laws are: Ø Kirchhoff’s voltage law: The sum of voltages around a closed path equals zero. Ø Kirchhoff’s current law: The sum of electric currents flowing from a node equals zero. Ø 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

Islamic University of Gaza Faculty of Engineering Electrical Engineering Department Ø 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: Ø 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

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

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

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

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

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

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

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

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 partialfraction expansion. Control Systems Design, Dr. Moayed Almobaied

Islamic University of Gaza Faculty of Engineering Electrical Engineering Department Partial-Fraction Expansion Ø If F 1(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. Ø 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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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