Course Overview Provides a background of control principles in various engineering applications. Basic mathematical tools such as Laplace transform, transfer function, block diagram, signal flow graph, mathematical modeling of dynamic systems, time response analysis, stability of linear system, root locus and frequency domain analysis are utilized. CO1 Ability to apply various mathematical principles (from calculus and linear algebra) to solve control system problems. CO2 Ability to obtain mathematical models for such mechanical, electrical and electromechanical systems. CO3 Ability to derive equivalent differential equation, transfer function and state space model for a given system. CO4 The ability to perform systems time and frequency-domain analysis with response to test inputs. Analysis includes the determination of the system stability. Final Examination :50% Lab Assessment :25% Mid-Semester Test :15% Assignments :10% Total Mark :100% Textbook i. Nise N.S. (2008). Control System Engineering (5th Ed), John Wiley & Sons. References ii. Ogata K. (2002). Modern Control Engineering (4th Ed), Prentice Hall. iii. Dorf R.C., Bishop R.H. (2001). Modern Control Systems (9th Ed), Prentice Hall. WeekCourse Content 1-2Introduction to Control Systems 3-4The Basics of Control Theory 5-6Mathematical Model of Systems 7-9System Stability 10-11Time-Domain Analysis 12-13The Root Locus Method 14Frequency Response Method 15Controller Introduction to Control System Basic Concepts Control System Examples Control System Design System A collection of components which are coordinated together to perform a function. Dynamic System A system with a memory. For example, the input value at time t will influence the output at future instant. A system interact with their environment through a controlled boundary. The interaction is defined in terms of variables. i. System input ii. System output iii. Environmental disturbances The systems boundary depends upon the defined objective function of the system. The systems function is expressed in terms of measured output variables. The systems operation is manipulated through control input variables. The systems operation is also affected in an uncontrolled manner through disturbance input variables. Control is the process of causing a system variable to conform to some desired value. Manual control Automatic control (involving machines only). A control system is an interconnection of components forming a system configuration that will provide a desired system response. Control System Output Signal Input Signal Energy Source Control is a process of causing a system variable such as temperature or position to conform to some desired value or trajectory, called reference value or trajectory. For example, driving a car implies controlling the vehicle to follow the desired path to arrive safely at a planned destination. i. If you are driving the car yourself, you are performing manual control of the car. ii. If you use design a machine, or use a computer to do it, then you have built an automatic control system. Transient response: Gradual change of output from initial to the desired condition Steady-state response: Approximation to the desired response For example, consider an elevator rising from ground to the 4 th floor. Component or process to be controlled can be represented by a block diagram. The input-output relationship represents the cause and effect of the process. Control systems can be classified into two categories: i. Open-loop control system ii. Closed-loop feedback control system Process OutputInput An open-loop control system utilizes an actuating device to control the process directly without using feedback. A closed-loop feedback control system uses a measurement of the output and feedback of the output signal to compare it with the desired output or reference. Actuating Device Process Output Desired Output Response Measurement Output ControllerProcessComparison Single Input Single Output (SISO) System Open-Loop Control System Missile Launcher System Closed-Loop Feedback Control System Missile Launcher System Desired Output Response Measurement Output Variables ControllerProcess Multi Input Multi Output (MIMO) System i. Power Amplification (Gain) Positioning of a large radar antenna by low-power rotation of a knob ii. Remote Control Robotic arm used to pick up radioactive materials iii. Convenience of Input Form Changing room temperature by thermostat position iv. Compensation for Disturbances Controlling antenna position in the presence of large wind disturbance torque i. Ancient Greece (1 to 300 BC) Water float regulation, water clock, automatic oil lamp ii. Cornellis Drebbel (17 th century) Temperature control iii. James Watt (18 th century) Flyball governor iv. Late 19 th to mid 20 th century Modern control theory The Vetruvian Man i. Pancreas Regulates blood glucose level ii. Adrenaline Automatically generated to increase the heart rate and oxygen in times of flight iii. Eye Follow moving object iv. Hand Pick up an object and place it at a predetermined location v. Temperature Regulated temperature of 36C to 37C Figure shows a schematic diagram of temperature control of an electric furnace. The temperature in the electric furnace is measured by a thermometer, which is analog device. The analog temperature is converted to a digital temperature by an A/D converter. The digital temperature is fed to a controller through an interface. This digital temperature is compared with the programmed input temperature, and if there is any error, the controller sends out a signal to the heater, through an interface, amplifier and relay to bring the furnace temperature to a desired value. Car and Driver Objective: To control direction and speed of car Outputs: Actual direction and speed of car Control inputs: Road markings and speed signs Disturbances: Road surface and grade, wind, obstacles Possible subsystems: The car alone, power steering system, breaking system Functional block diagram: Time response: Measurement, visual and tactile Steering Mechanism Automobile Driver Desired course of travel Actual course of travel Error + - Consider using a radar to measure distance and velocity to autonomously maintain distance between vehicles. Automotive: Engine regulation, active suspension, anti-lock breaking system (ABS) Steering of missiles, planes, aircraft and ships at sear. Control used to regulate level, pressure and pressure of refinery vessel. For steel rolling mills, the position of rolls is controlled by the thickness of the steel coming off the finishing line. Coordinated control system for a boiler- generator. Consider a three-axis control system for inspecting individual semiconducting wafers with a highly sensitive camera i. CD Players The position of the laser spot in relation to the microscopic pits in a CD is controlled. ii. Air-Conditioning System Uses thermostat and controls room temperature. i. System, plant or process To be controlled ii. Actuators Converts the control signal to a power signal iii. Sensors Provides measurement of the system output iv. Reference input Represents the desired output Sensor Actuator Process Controller + + Set-point or Reference input Actual Output Error Controlled Signal Disturbance Manipulated Variable Feedback Signal 1. Establish control goals2. Identify the variables to control3. Write the specifications for the variables4. Establish the system configuration and identify the actuator5. Obtain a model of the process, the actuator and the sensor6. Describe a controller and select key parameters to be adjusted7. Optimize the parameters and analyze the performanceIf the performance meet the specifications, then finalize design If the performance does not meet specifications, then iterate the configuration and actuator Application: CD player, computer disk drive Requirement: Constant speed of rotation Open loop control system: Block diagram representation: Closed-loop control system: Block diagram representation: Goal of the system: Position the reader head in order to read data stored on a track. Variables to control: Position of the reader head Specification: i. Speed of disk: 1800 rpm to 7200 rpm ii. Distance head-disk: Less than 100nm iii. Position accuracy: 1 m iv. Move the head from track a to track b within 50ms System Configuration: