Design_Project_Week1_Sp10_TA version1WEEK 1Introduction:The WindDrive Electric GeneratorDesign_Project_Week1(SP_10)TA_edition2WEEK 1Introduction:The WindDrive Electric GeneratorCircuit Diagram :Department of Mechanical Engineering Michigan State University East Lansing, MI 48824-1226 ME451 Laboratory PI CONTROL DESIGN PROJECT WEEK 1 Bring the course textbook to the Lab ‘C.L.Philips and R.D.Harbor, Feedback Control Systems’ NOTE: It maybe helpful to look at the following in the course textbook before coming to the lab: Chapter 7: Sections 7.1 to 7.5 Section 7.10 ME451 Laboratory Manual Pages, Last Revised: April 8, 2011 Send comments to: Dr. Clark Radcliffe, Professor1 Introduction: As stated in the Whirlwind memorandum of January 18, the Residential Wind Power Development Group is dedicated to the development of the new WindDrive wind powered electric generator for residential use. In the previous months we have investigated various techniques related to control systems analysis and design because we feel that the ability to accurately control a process is vital to high technology product performance. We have verified the mathematical model that governs the response of the DC servomotor, and are now ready to apply these tools to design a speed control system. We will test the control design process on the servomotor in lab because it is a good physical model to serve in place of the WindDrive electric generator. After you finalize your design, your design will be tested by Whirlwind technicians to see if it meets performance specifications. The WindDrive Electric Generator The WindDrive electric generator (Fig. 1) has an electrical voltage output eg(t) that is determined by a combination of wind speed vw(t) and propeller angle of attack αg(t). Figure 1: The WindDrive Residential Wind Powered Electric Generator Prototype τvw,αg( ) ω Wind Speed vw(t), Propellor Speed ω and Applied Torque τvw,αg( ) J Generator and Propellor with Inertia Jand Friction B B vw(t) eg Constant Field Figure 2. The WindDrive Wind Turbine2 The turbine propeller blade airfoil rotates at speed ωθ= with angle of attack αg(t) (Fig. 3). The propeller’s effective angle of attack is reduced by the propeller’s rotation speed ω and determines the Lift force L and torque T on the generator. This torque generated is proportional to the product of this angle and the wind velocity. As the wind speed varies, we can use feedback control (Fig. 2) of propeller angle of attack αg(t) to control the system’s electrical voltage output eg(t). Instead of the voltage being regulated to control motor speed, the wind turbine angle of attack α will be regulated to control the generator speed and resulting voltage. The torque applied to the generator, T = rL = kliftvwαrel= Kwindαg− rω( ) (1) where Kwind= kliftvwis a wind speed dependent coefficient for the airfoil andr is the radius of the center of lift on the propeller blades. Following the derivations in the text [Phillips and Harbor section 2.72], the wind generator rotation speed ω produces the electrical potential eg= Kgω (2) through the generator’s emf constant Kg. The generator’s speed is modeled by JBTωω+= (3) Taking the Laplace Transform of (1)&(3) and substituting (1) into (3) yields the system model, Js + B + rKwind( )Ω(s) = Kwindαg(s) (4) Now using this result in the Laplace transform of (2) yields the system model Eg(s) =KgKwindJs + B + rKwind( )αg(s) (5) This model has the transfer function αg rω vw vrel Lift Force L produces Torque T = rL = kliftvwαrel= rkliftvwαg− rω( ) Figure 3. Angle of Attack3 G(s) =Eg(s)αg(s)=KgKwindJs + B + rKwind( ) (6) This transfer function is a standard 1st order form )1()()()(+==sKsRsCsGτ (4-2) = (7) whereC(s) = Eg(s)and R(s) =αg(s)are the Laplace transforms of the output and input variables, respectively, the DC gainK = KgKwind( )B + rKwind( ), and the time constant τ= J B + rKwind( ). This is the same form as the transfer function we have identified for our servo motor in previous laboratory exercises. Objective: The objective of this project is to design a PI (Proportional-Integral) controller to improve the transient response of the DC servomotor used in experiments 1 and 4 and demonstrate that we can control the transient response of our new product. As in experiments 1 and 4, we will represent this motor as a first-order system. This assumption has been tested in the aforementioned experiments, and found to be acceptable. The concept of root locus described in the controls textbook is essential for designing of the PID class of controllers. As such we will be relying heavily on its use. DC Servo Motor and the PI controller: The block diagram for the WindDrive electric generator speed controller is shown below where Co is the desired speed, ∆C is the deviation from the desired speed, Ao is the nominal actuation to the plant, and ∆A is the change in actuation to compensate for ∆C. Figure 8. Block Diagram for PI Speed Control System In an open-loop system, the nominal output ooGAC = so that when the desired output oCR =, the nominal actuation K G CCsCo∆+=)( oCsR =)( CE ∆−= A∆ oA AAAo∆+= c4 RKCGAoo==11 where K is the steady-state gain of the DC motor at its operating point. For our work here, no corrective measures would be taken for deviations from the desired speed resulting from disturbances to or variations in the system. Most block diagrams in the class textbook do not include a nominal actuation. The reason for this is that most examples in the book use an operating point of zero; hence the nominal actuation does not appear. For small deviations from the operating point, the block diagram presented in Figure 8 can be simplified to the deviation block diagram used for our analysis and PI controller design. Figure 9. Simplified Block Diagram for PI Controller Design In this block diagram R(s) is a combination of a bias level with a square wave representing changing operating points of a fixed variation about a desired mean speed (Volts). C(s) is the tachometer output of the motor (Volts), G is the plant transfer function given by (7). From the first laboratory experiment, the model for the plant was determined to be )13.0(8.0)1()(+=+=ssKsGτ (8)
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