WEEK 21ME 451: Control Systems Laboratory Department of Mechanical Engineering Michigan State University East Lansing, MI 48824-1226 ME451 Laboratory TORSIONAL CONTROL DESIGN PROJECT WEEK 2 Bring the course textbook to the Lab ‘C.L.Philips and R.D.Harbor, Feedback Control Systems’ ME451 Laboratory Manual Pages, Last Revised: April 10, 2010 Send comments to: Dr. Clark Radcliffe, Professor2 B J θ,τ k b Figure 3: Schematic Diagram of WindDrive Support Structure Introduction: The ability to accurately control a process is vital to high technology product performance. Whirlwind Corporation is primarily interested in the potential performance increase that can be obtained in its new residential WindDrive electric generator product line. Reduction in vibration transmitted to the transmission shaft and increased efficiency due to lower controller effort are potential benefits Whirlwind would like to achieve. Also, precise positioning and vibration control is necessary for proper functioning of the vane angle control and subsystems. Other application examples include the automobile suspension system or a laser positioning system for machining. In the second experiment you and your colleagues verified the mathematical model that governs the response of a MSD system. Your task this week is to design a torsion control system. After finalizing the design we will have the design tested by Whirlwind technicians to see if it meets performance specifications. The Wind Drive Electric Generator The structure of our WindDrive wind powered electric generator will be subject to torsional vibration. The generator module is supported on a tall support tube (Fig. 1). The generator module on the top of this tube is massive (Fig. 2). The support structure will be subject to torsional vibration from the interaction between the rotating generator blades and the support tube. This rotational vibration will subject the generator’s support bearings to fatigue loading substantially reducing bearing life. We propose to mount an inertial torque actuator within the generator module to control torsional vibration. A simple schematic torsional vibration model (Fig. 3) indicates the important components contributing to structural torsional vibration. The equations of motion for this system is τθθθ=++ kbJ&&& (1) where J is the rotational inertia of the generator module, B is the small damping provided by air friction on the generator blades and body and K is the torsional stiffness of the support tube. Figure1: The WindDrive Figure 2: The Supported WindDrive Generator Module3 This equation of motion generates the same transfer function form as that used to describe the dynamics of the torsional vibration experiment you have used in the laboratory G(s) =θ(s)T (s)=1Js2+ bs + k (2) Because the WindDrive and torsional vibration apparatus have models of the same form, the research team will use the torsional vibration apparatus to investigate vibration control designs for our new2 product. Objective: The objective of this project is to design a PD (Proportional-Derivative) controller for improving the transient response of a second order system. The second order system in this case is the Mass Spring Damper system used in experiments 2 and 5. This system will be used to model the support dynamics of the WindDrive system. The concept of root locus described in the controls textbook is an effective method for designing the PID class of controllers. In this project we will focus on the PD controller. Torsional MSD System and the PD Controller: The torsional control system has the block diagram Figure 4: Closed-Loop Torsional Control Block Diagram showing the Open-Loop System Blocks as a Subsystem of the Closed-Loop System Block Diagram. The parameters in the system are: Table 1: Torsional Vibration System Parameters Parameter Value (Units) J 0.008 ± 0.002 (kg-m2) b 0.025 ± 0.015 (N-m-sec.) k 1.6 ± 0.2 (N-m/rad) ek 25 (volt/rad) hk 0.8 (N-m/volt) The design of a controller for systems like the one above (Fig. 4) is discussed in Section 7.10 of the Phillips and Harbor Feedback Control Systems text. In this section, control design is performed on the open-loop transfer function defined when the comparator + Dθ sKKDP+ ek hk kbsJs++21 E θ A Open-Loop System4connection is broken in Figure 4 above. When the parameters above are substituted into the block diagram above, the open-loop transfer function kGH =θ(s)θD(s)=KP+ KDs()kekhJs2+ bs + k (3) This open-loop transfer function depends on the controller parameters, KP and KD, assumed to be positive numbers. The open-loop transfer function can take parameter values anywhere in the indicated ranges. Although the design of a stable control system response is performed on the open-loop transfer function, the closed-loop response of controlled system will be verified with analytical prediction of closed-loop response using the Closed-Loop Transfer function T (s) =θ(s)θD(s)=kG1 + kGH=KP+ KDs()kekhJs2+ bs + k1 +KP+ KDs( )kekhJs2+ bs + k=KP+ KDs( )kekhJs2+ KDkekh+ b( )s + KPkekh+ k( ) (4) This closed-loop transfer function again depends on the controller parameters, KP and KD, assumed to be positive numbers. The closed-loop response of controlled system will be verified with analytical prediction of closed-loop response using this Closed-Loop Transfer function. Whirlwind Torsion Control Design: We will first investigate the case of Proportional Control for designing a controller for the mass-spring-damper system that will be used to model the WindDrive transmission shaft [Phillips & Harbor, section 7.10.1]. Finally, we will investigate Proportional and Derivative Control [Phillips & Harbor, 7.10.3]. Whirlwind lab consultants will test your design to see if they produce acceptable results.5Torsional Control Design Project – Week 2 Refer to the Torsional MSD system and the PD controller section for the Block Diagram and the values of the parameters of the system. Name: Section: Date: The torsional control system has the block diagram PART I. Proportional Controller Design (
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