1. Introducation to Linear Control Systems.pptx

Linear Control Systems

Linear Control SystemsObaid SabirAssistant Professor

Department of Electrical Engineering

1Obaid Sabir, Spring-2015Control systems plays a vital role in our day-to-day lifeProvides 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.

Introduction to Control Systems22Obaid Sabir, Spring-2015Basic DefinitionsSystem: an arrangement or combination of different physical components that are connected or related together to form an entire unit to achieve/perform a certain objective Systems can be physical, economical, biologicalControl: to regulate, direct or command a system so that a certain output is achieved. Control system: interconnection of components to provide a desired function

33Obaid Sabir, Spring-2015Plant: a piece of equipment, set of machines functioning together to perform a particular operation. Any physical object to be controlled.E.g.: Mechanical devices, heating furnace, spacecrafts.Process: Progressively continuing operation which occurs in a series of controlled actions systematically towards a particular result. Any operation to be controlled.E.g.: Navigation on aircraft.44Obaid Sabir, Spring-2015Input: applied signal or excitation signal that is applied to a control systemOutput: The actual response that is obtained from a control system due to the application of the inputPlant is fixed. Output produced is fixed.Block Diagram: identifies the major components of the systems in the form of blocks. Shows the direction of information and energy flow from one component to anotherBasic ComponentsPlant / ProcessOutputs(Results)Inputs(Objective)55Obaid Sabir, Spring-2015DisturbancePlant with ControllerPlant / ProcessOutputs(Results)Inputs(Objective)ControllerController: a component of the system which generates a manipulated signal to the input to produce a desired output.Disturbance: a signal that tends to affect the value of the output of a system.Internal Disturbance: vibration, soundExternal Disturbance: Wind, surroundings, noises.Actuators: Apply force or torque to the physical systemSensor: Measure system behavior. 66Obaid Sabir, Spring-2015ExamplesCruise Control in Cars:Automobile is the PlantThe actuator is the engine which generates propulsive forces that turn the wheelThe Sensor is the tachometer, which measures the vehicle speed

Other example:Climate controlTraction controlIndustrial Automation (Assembly lines)RoboticsSolar Trackers7Output SignalTransient: instantaneous change of the input against the gradual change of output. Physical system undergoes gradual change of state.Steady State: Approximation to the command or desired response. Occurs when system near the desired output.

8Advantages of Control SystemsWe build control systems for four primary reason:Power Amplification (Gain)Positioning of a large radar antenna by low-power rotation of a knobRemote ControlRobotic arm used to pick up radioactive materialsConvenience of Input FormChanging room temperature by thermostat positionCompensation for DisturbancesControlling antenna position in the presence of large wind disturbance torque9Classification of Control SystemsDepending on the relation of the control action with the output, any control system can be classified as:Open - loop systemClosed - loop system10Open Loop SystemsOutput has no effect on the control actionOutput value is not measured, isolated from inputOperates on the basis of time.Examples: bread toaster, hand drier, traffic signals, man walking with eyes closed

11Example of Open Loop SystemWashing Machine:Soaking, washing and rinsing is time operated.Machine does not measure the output signal, cleanliness of clothes.Output signal is not compared with the inputFixed operating conditions (time)Accuracy depends on calibration12Advantages of Open LoopSimple in construction and designUsed where inputs are known, disturbance is minimum and outputs are difficult to measureEconomic as low in cost and low power consumptionsEasy to maintain

13Disadvantages of Open LoopNot accurate and reliableAccuracy depends on the accuracy of calibrationOptimization is not possibleExternal disturbances effect the system producing inaccurate resultsChanges in parameters require constant recalibration

14Closed Loop SystemsControlling action is dependant on the output or changes in inputOutput is fed back into the inputFeedback signal produces error signal

15Error Signal [e(t)]: Difference between the input and the feedback signal. Fed into the controller to reduce the error and bring the output of the system closer to the desired value.Input transducer sense the input physical quantity and converts it into a form to be used by the controller [r(t)]Controlled Variable [c(t)]: quantity which is controlledManipulated Variable [u(t)]: quantity which is variedOutput transducer measure the output response and convert it into a form used by the controllerOutput signal arrives back via a feedback pathSumming junction: algebraically sums two or more signals

Closed Loop Systems Definitions16Advantages of Closed LoopResponse is more accurate due to correction of arising errorsInsensitive to external disturbancesTransient response and steady state response can easily be controlledReduced effects of non-linearity High bandwidth, higher operating frequency zones17Disadvantages of Closed LoopComplicated in designComplex and costlierOscillations generates within the systemCan get unstable in certain conditions18A Manual Level Control System

19Example of Closed LoopObjective: To control direction and speed of carOutputs: Actual direction and speed of carControl inputs: Road markings and speed signsDisturbances: Road surface and grade, wind, obstaclesPossible subsystems: The car alone, power steering system, breaking system

20Functional block diagram:

Time response:

Measurement, visual and tactileSteering MechanismAutomobileDriverDesired course of travelActual course of travelError+-21Types of Feedback:Positive feedback:When a system tends to increase outputSmall disturbances increase the magnitude of perturbations (Changes in normal State)Tends to cause system instabilityResults in exponential growth, increasing oscillations

Examples: Camera pointed to screen, Amplifier oscillations in electronics, microphone and speaker resonance, Computer and social networks.

22Negative Feedback:System tends to reduce outputResults of a process causes the operation to reduce changeMakes system self regulating, more stableReduces the effects of fluctuationsTypes of Feedback:

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