Lec 1 Introduction to Control Systems Systems PDF

INTRODUCTION TO CONTROL SYSTEMS Course: EE311 Fundamentals of control Date: 4/10/2023 Contents Course Description Control System Definition Control System Examples Control System Parameters Control System Types Laplace Introduction  Introduction to control system Mode...

INTRODUCTION TO CONTROL SYSTEMS Course: EE311 Fundamentals of control Date: 4/10/2023 Contents Course Description Control System Definition Control System Examples Control System Parameters Control System Types Laplace Introduction  Introduction to control system Modelling of mechanical systems Modelling of electrical systems COURSE Modelling of electromechanical systems DESCRIPTION Block diagram reduction and application Signal flow graph modelling and application Control system response to different inputs 3  Time response analysis Error analysis and system type COURSE Stability analysis using Routh-Hurwitz DESCRIPTION stability criterion Root locus technique and application 4  7th Week (30 Marks) 5th Week Exam (15 marks) 7th Week Exam (15 marks) 12th Week (20 Marks) COURSE 10th Week Exam (10 marks) DESCRIPTION 12th Week Exam (10 marks) Assessment (10 marks) Sheets (4 marks) Report/Presentation/Project (6 marks) 5 CONTROL SYSTEM DEFINITION Control System Definition A system that uses a certain control strategy to produce desired results according to specific objectives such as: Robotic systems Temperature, Pressure and humidity control in any industrial operations The objective of the control system is to control the outputs by the inputs through the control system elements The control system components are the objectives (also called inputs, or actuating signal 𝒖), and the results (also called outputs, or controlled variables 𝒚) 7 CONTROL SYSTEM EXAMPLES Centrifugal Speed Governor The first automatic control system used in the industry is agreed to be James Watt’s centrifugal governor, which was developed in 1769 The governor is used to control the speed of a steam engine The input is the shaft speed, the output is the valve angle, and the controlled process is the Steam Engine 9 Idle-speed control of an automobile The objective is to maintain the engine idle-speed at a relatively low value regardless of the applied engine loads for fuel economy Car Engine Engine loads are the air conditioning, power steering, transmission, power brakes, … etc. The system inputs are the throttle angle 𝜶 and the load torque 𝑻𝑳 , and the output is the engine speed 𝝎 and the 𝛼 Control 𝜔 controlled process is the engine. 𝑇𝐿 system 11  Sun tracking control of solar collectors The objective is controlling the collector dish to track the sun during daylight, which improves the electricity generation required for water extraction. The controller inputs are the sun rate and sun sensor, the outputs are motor commands, and the process is the Dish Sun rate Control Motor system Sun sensor 12 Embedded control systems On-board special purpose digital computer serves complex integral components of the feedback loop A rover is an example for systems which use an onboard embedded computer Sensors are optical encoder for measuring engine speed, a rate gyro and accelerometer to measure turns, and GPS unit to obtain position and velocity estimates of the vehicle Actuators include two linear actuators to turn the front wheel and to brake and accelerate Communication devices permits the rover to stay in contact with the ground station. 13 CONTROL SYSTEM PARAMETERS Control System Parameters Controlled Variable is the quantity or condition that is measured and controlled. Normally, the controlled variable is the output of the system. Control Signal or Manipulated Variable is the quantity or condition that is varied by the controller to affect the value of the controlled variable. Actuator is the unit that directly affect the controlled variable as a result of the control signal. Control means measuring the value of the controlled variable of the system and applying the control signal to the system to correct or limit deviation of the measured value from a desired value. Processes (1) is a continuing development marked by a series of changes in a relatively fixed way and lead toward a particular result or end, (2) is a progressively continuing operation that consists of a series of controlled actions or movements systematically directed toward a particular result or end. Examples are chemical, economic, and biological processes. 15 Control System Parameters Systems is a combination of components that act together and perform a certain objective. Disturbances is a signal that tends to adversely affect the value of the output of a system. If a disturbance is generated within the system, it is called internal, while an external disturbance is generated outside the system and is an input. Feedback Control refers to an operation that, in the presence of disturbances, tends to reduce the difference between the output of a system and some reference input and does so based on this difference. 16 CONTROL SYSTEM TYPES Types of Control Systems Open loop control systems (Non-feedback systems) When the output has no effect on the control action it is called an open-loop control systems. In other words, in an open loop control system the output is neither measured nor fed back for comparison with the input. Example: Washing machine (operate on a time based control) Closed loop control (Feedback control systems) In a closed-loop control system the actuating error signal, which is the difference between the input signal and the feedback signal (which may be the output signal itself or a function of the output signal and its derivatives and/or integrals), is fed to the controller so as to reduce the error and bring the output of the system to a desired value. Example: Air conditioning (operates on sensing the temperature) 18 Open Loop Control System Actuating Reference Control signal 𝑢 Controlled Controlled input 𝑟 system process variable 𝑦 General block diagram 𝛼 Control 𝑇𝐿 system Car Engine 𝜔 Engine Example Description Example block diagram 19 Open Loop Control System Battery CD Player requires a constant speed rotation DC motor is used an actuator, since the output speed is proportional to Rotating disk the applied voltage input The disk is the process which requires constant speed DC DC motor The controller in this case is the Speed setting amplifier amplifier Control system block diagram Desired speed Rotating (Voltage) Amplifier DC motor Output speed disk 20 Closed Loop Control System Open Loop response Closed Loop response 𝑇𝐿 applied 𝑇𝐿 applied Idle Idle Engine Error = 0 Error Engine speed speed Car Engine Closed loop block diagram 𝑇𝐿 + 𝜔𝑟 𝜔𝑒 Control + 𝜔 Engine + system − Speed Car Engine transducer 21 Closed Loop Control System Battery Closed loop rotating disk application is by adding a tachometer as a speed sensor. Rotating disk The output of the tachometer is then subtracted from the desired speed DC Speed DC The amplifier in this case is acting on setting + amplifier motor the error, which can reduce the error − Tacho- in case of any external disturbances meter Control system block diagram Error Desired speed DC Amplifier Rotating disk Actual speed (Voltage) + motor − Measured speed (voltage) Tachometer 22 Closed Loop Control System The Hard disk drive (HDD) is an example for a closed loop system The objective is to move the reader head to read data stored on a track on the disk The reader head position is the control variable Control system block diagram Error Desired head Control Actuator motor Actual head position + device and read Arm position − Sensor 23  Comparison Between Open Loop And Closed Loop Control OPEN LOOP CLOSED LOOP A non-feedback system in which the output can be changed to any desired A feedback control system in which the desired output is maintained by being value by appropriately changing the input signal. However, the output is measured and fed back to be compared with the input signal. The error and control Definition neither measured or fed back so it has no influence or effect on the control signals are then produced, hence the control action is dependent on the output in action of the input signal. some way. Block Diagram Simple implementation Knowledge of the output condition leads to; Satisfactory performance with good calibration Reduced error Advantages Accurate reliable and repeatable performance Robust against system disturbances No knowledge of the output condition leads to: More complex in implementation with one or more feedback paths Absence of self-correct which may lead to high errors. The feedback introduces the possibility of undesirable system oscillations (hunting) Disadvantages High sensitivity to disturbances i.e. variations in external conditions or as the controller tries to over-correct itself. internal system parameters may cause output to vary from desired value in Less stable comparatively uncontrolled fashion. Traffic control system Speed control system Applications Electric washing machine Temperature control system Control for coal heating in furnaces Pressure control system 24  Linear Nonlinear The control system is The control system is linear when the nonlinear when the system components system components exhibit linear exhibit nonlinear characteristics to the characteristics to the Linear Vs. control system signals control system signals magnitude magnitude Nonlinear Simple analysis Complex analysis Example: 𝑦 = 𝑥 Example: 𝑦 = sin 𝑡 2 1 1.5 1 0.5 y y 0.5 0 0 0 1 2 0 2 x t 25  Time-Invariant Systems Time-Varying Systems Time-Invariant Vs. The system The system parameters are parameters are Time-Varying stationary with varying with respect systems respect to time to time Simple analysis Complex analysis Example: Example: 𝑦(𝑡) = 2𝑢(𝑡) + 2 𝑦(𝑡) = 8𝑢(𝑡) + 2𝑡 26 Continuous- Data Control Systems (DC) 27 Continuous- Data Control Systems (AC) 28 Discrete-Data Control System 29 LAPLACE TRANSFORM INTRODUCTION  Laplace Introduction Given the real function 𝑓 𝑡 that satisfies the condition ∞ න |𝑓 𝑡 𝑒 −𝜎𝑡 |𝑑𝑡 < ∞ 0 For some finite, real 𝜎, the Laplace transform of 𝑓(𝑡) is defined as ∞ 𝐹 𝑠 = න 𝑓 𝑡 𝑒 −𝑠𝑡 𝑑𝑡 0 The variable 𝑠 is referred to as Laplace operator, which is a complex variable; that is 𝑠 = 𝜎 + 𝑗𝜔, where 𝜎 is the real component and 𝜔 is the imaginary component. 31 Laplace Introduction Example (1): Let 𝑓 𝑡 be a unit-step function that is defined as 𝑢 𝑡 = 1, 𝑡≥0 𝑓 𝑡 =ቊ 𝑠 0, 𝑡