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### 1271Sol_final3

Course: MATH 1271, Fall 2009
School: Minnesota
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Minnesota - MATH - 1271
The Mean Value Theorem and the Extended Mean Value TheoremWillard Miller September 21, 20060.1The MVTRecall the Extreme Value Theorem (EVT) from class: If the function f is defined and continuous on a closed bounded interval [a, b] then there is some
Minnesota - MATH - 1271
B g Bg BqqT BqqT t nm mdd| d ybobR TylDrjnmq jim1XbogjgbbjndiTogbim1Xbgicfw_%) nm lk mt mk h m mt mk h d lk n 0Bg BqT jBqgBqT8 i nm lk m| h w m m| h w d lk n yo~mepogXybpRkbbjnibbIjkbig0~me)bIiX% 0B iBqT jBWBqT8 n lk i nm i d lk n yiom1bom&amp;gbhboi2bjhxgX
Minnesota - MATH - 1271
Minnesota - MATH - 1271
Math 1271 Solutions for Fall 2005 Final Exam2 2 xy1) Since the equation x + y = e cannot be rearranged algebraically in order to write y as an explicit function of x , we must instead differentiate this relation implicitly with respect to x , in order t
Minnesota - MATH - 1271
Minnesota - MATH - 1271
Math 1271, Lec 020: Calculus I Fall 2010 Midterm Exam IIInstructions Check that this booklet consists of 10 pages including the front page. To get full credit, you must show all steps in your solutions. Calculators are NOT allowed. You don't need to sim
Minnesota - MATH - 1271
Math 1271, Lec 020: Calculus I Fall 2010 (Practice) Midterm Exam IIInstructions Check that this booklet consists of 10 pages including the front page. To get full credit, you must show all steps in your solutions. Calculators are NOT allowed. You don't
Minnesota - MATH - 1271
Minnesota - MATH - 1271
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Minnesota - MATH - 1271
Math 1271, Lec 020: Calculus I Fall 2010 Midterm Exam IIIInstructions Check that this booklet consists of 8 pages including the front page. To get full credit, you must show all steps in your solutions. Calculators are NOT allowed. You don't need to sim
Minnesota - MATH - 1271
Math 1271, Lec 020: Calculus I Fall 2010 (Practice) Midterm Exam IIIInstructions Check that this booklet consists of 10 pages including the front page. To get full credit, you must show all steps in your solutions. Calculators are NOT allowed. You don't
Minnesota - MATH - 1271
Minnesota - MATH - 1271
Minnesota - MATH - 1271
0.1Newton's method and the Mean Value TheoremNewton's method for computing the zeros of functions is a good example of the practical application of the Mean Value Theorem. Let f (x) be a realvalued function on the real line that has two continuous deriv
Minnesota - ME - 8281
Chapter 2Stability ConceptsIn this chapter, we discuss two notions of stability, namely input/output (I/O) stability, and internal (or Lyapunov) stability. They are related, but not exactly the same. The latter is more of a statespace concept, whereas t
Minnesota - ME - 8281
Chapter 6Linear Quadratic Optimal Control6.1 IntroductionIn previous lectures, we discussed the design of state feedback controllers using using eigenvalue (pole) placement algorithms. For single input systems, given a set of desired eigenvalues, the f
Minnesota - ME - 8281
Chapter 7Kalman FilterIn this chapter, we study Kalman Filtering, which is a celebrated &quot;optimal&quot; observer/filter/prediction design method. In many ways, Kalman filter is the dual of LQ control. We shall develop Kalman filter in this way. Recall that fo
Minnesota - ME - 8281
Chapter 8Internal Model Principle and Repetitive ControlIn this chapter, we look at disturbance rejection and reference tracking in which the disturbances or reference signals have known structure - namely they can be thought of as being generated by an
Minnesota - ME - 8281
Chapter 9Reference Input Tracking: feedforward control9.1 IntroductionIn previous lectures, we have discussed control designs based on actual or observer estimated state feedback, eigenvalue (pole) assignments, as well as controllers based on internal
Minnesota - ME - 8281
Chapter 1Linear Dynamical Systems1.1 System classifications and descriptionsA system is a collection of elements that interacts with its environment via a set of input variables u and output variables y. Systems can be classified in different ways.Con
Minnesota - ME - 8281
Department of Mechanical Engineering University of Minnesota ME8281 Advanced Control Systems Spring 2012 Prof. Perry Li Assignment #1. Assigned: Feburary 3, 2012 (Friday) Due: February 15, 2012 (Wednesday) 1. (Modeling Hydraulic Hybrid Vehicle) The hydrau
Minnesota - ME - 8281
ME 8281 Advanced Control Systems Design Department of Mechanical Engineering University of Minnesota Spring 2012Instructor: Perry Li Office: MechE 309 Email: perry-li@umn.edu Tel: 612-626-7815 Class schedule:WF 10:10-12:00 Office Hours: Tu 2:00-3:00pm (t
Minnesota - ME - 4231
Minnesota - ME - 4231
Minnesota - ME - 4231
Minnesota - ME - 4231
Minnesota - ME - 4231
Minnesota - ME - 4231
Minnesota - ME - 4231
LAB 8 PID ControlRajesh RajamaniME 4231 Department of Mechanical Engineering University Of MinnesotaREVISITING P-CONTROLydese C u P yClosed-loop transfer function isK p Km Y (s) Ydes ( s ) s2 K p Km 1 s Tm Tm TmFor good damping 1 Kp 1 4 K mTm1
Minnesota - ME - 4231
LAB 11 INTRODUCTION TO PLCsRajesh RajamaniME 4231 Department of Mechanical Engineering University Of MinnesotaPLCsUser Entered ProgramInputsOutputsA PLC (Programmable Logic Controller) works by looking at its inputs, and depending upon their stat
Minnesota - ME - 4231
LAB 10 Mobile Robot ControlRajesh RajamaniME 4231 Department of Mechanical Engineering University Of MinnesotaOBJECTIVESLab ObjectiveTo design and implement a motion control system for a wheeled mobile robot Moving to a desired position Translation a
Minnesota - ME - 4231
ME 4231 Lab 10 Mobile Robot Control 1. Lab Objective The objective of this lab is to design and implement a motion control system for a mobile robot. The developed controller has to ensure that the robot can follow a designed trajectory and also determine
Minnesota - ME - 4231
Minnesota - ME - 4232
Pilot-to-open check valve with standard pilotFunctional Group: Products : Cartridges : Pilot-to-Open Check : 3-Port, Non-Vented : Standard Pilot, Steel SeatCapacity: 7.5 gpm (30 L/min.) Model: CKBB-XCNProduct Description This valve is a pilot to open c
Minnesota - ME - 4232
ME 4232: FLUID POWER CONTROLS LABClass Cl #1 Introductions &amp; Fluid Power FundamentalsClass Agenda Introductions Fluid Power Introduction Syllabus Fluid Power Fundamentals Least Squares Fitting Summer Opportunities Course Goals5Peer Introductions Nam
Minnesota - ME - 4232
ME4232: Fluid Power Controls Lab Pressure Compensated Flow Control ValveJim Van de VenIn the figure is a Pressure-Compensated Flow-Control (PCFC) valve in a hydraulic circuit. In a group of 2 or 3, discuss and answer the following questions: 1. Identify
Minnesota - ME - 4232
ME 4232: FLUID POWER CONTROLS LABClass #2 Fluid Power FundamentalsNotes Syllabus Questions? Upcoming Labs: Lab 4: Pressure Compensated Flow Control Valve Lab 5: Relief Valves (Direct &amp; Pilot Operated)2Agenda Review: Momentum, Continuity, Constituti
Minnesota - ME - 4232
ME4232: Fluid Power Controls Lab Series &amp; Parallel CircuitsJim Van de VenCircuit #1: Single ValveP2 Q1 P1 Q2 P3 Needle Valve P0 P4Circuit #2: Valves in SeriesP2 Q1 P1 P3 Q3 P0 N2 P4 Q2 N1Circuit #3: Valves in ParallelP2 Q1 P1 Q3 N1 N2 Q2P0P4ME42
Minnesota - ME - 4232
ME 4232: FLUID POWER CONTROLS LABClass Cl #3 Valves and Simple Circuit AnalysisNotes Video Captures Online Moodle for Grades Upcoming Labs: Lab 6: Meter-in / Meter-out Circuits Lab 7: Check Valves: Direct &amp; Pilot Operated p2Agenda Hydraulic Circuit
Minnesota - ME - 4232
Free flow side to nose check valveFunctional Group: Products : Cartridges : Check : 2-Port : Free Flow Side to NoseCapacity: 15 gpm (60 L/min.) Model: CXCD-LANProduct Description Free-flow, side-to-nose check valves are on/off circuit components that a
Minnesota - ME - 4232
Free flow nose to side check valveFunctional Group: Products : Cartridges : Check : 2-Port : Free Flow Nose to SideCapacity: 20 gpm (80 L/min.) Model: CXDA-LANProduct Description Free-flow, nose-to-side check valves are on/off circuit components that a
Minnesota - ME - 4232
Fully adjustable pressure compensated flow control valve with reverse flow checkFunctional Group: Products : Cartridges : Flow Control : 2 Port : Fully Adjustable, Pressure Compensated, with Reverse Flow CheckCapacity: 12 gpm (45 L/min.) Model: FDCB-KAN
Minnesota - ME - 4232
Fully adjustable pressure compensated flow control valve with reverse flow checkFunctional Group: Products : Cartridges : Flow Control : 2 Port : Fully Adjustable, Pressure Compensated, with Reverse Flow CheckCapacity: 12 gpm (45 L/min.) Model: FDCB-LAN
Minnesota - ME - 4232
High accuracy closed center, flow divider-combiner valveFunctional Group: Products : Cartridges : Flow Divider : Divider/Combiner : Closed Center - High AccuracyCapacity: .6 - 3 gpm (2,5 - 12 L/min.) Model: FSBA-XANProduct Description Closed-center flo
Minnesota - ME - 4232
Closed center, flow divider-combiner valveFunctional Group: Products : Cartridges : Flow Divider : Divider/Combiner : Closed CenterCapacity: 1.5 - 8 gpm (6 - 30 L/min.) Model: FSCA-XANProduct Description Closed-center flow divider/combiners are sliding
Minnesota - ME - 4232
Flow divider valveFunctional Group: Products : Cartridges : Flow Divider : Divider : Divide OnlyCapacity: 1.5 - 8 gpm (6 - 30 L/min.) Model: FSCD-XANProduct Description Flow dividers are sliding-spool, pressure-compensated devices used to split oil flo
Minnesota - ME - 4232
ME 4232: Fluid Power Control LabUniversity of Minnesota Prof. Perry Y. LiLab. 1: Fluid Power Control Lab. Orientation ObjectivesTo be acquainted with the fluid power test bench and its components; and to be sure that the safety procedures are adhered t
Minnesota - ME - 4232
ME 4232: Fluid Power Control LabUniversity of Minnesota Prof. Perry Y. LiLab 2: Cylinder actuator ObjectiveTo study the flow rate / speed relationship of a cylinder actuator and to gain experience in using MATLAB for data analysis. Specifically, you wi
Minnesota - ME - 4232
ME 4232: Fluid Power Control LabUniversity of Minnesota Prof. Perry Y. LiLab. 3: Pressure-flow relationship across a needle valve ObjectiveTo study and characterize a needle valve. A needle valve is an adjustable orifice used to vary the flow in differ
Minnesota - ME - 4232
ME 4232: Fluid Power Control LabUniversity of Minnesota Prof. Perry Y. LiLab 4: Pressure compensated flow control valve ObjectivePressure compensated flow control valves are used to maintain constant flow rates in parts of the circuit irrespective of t
Minnesota - ME - 4232
ME 4232: Fluid Power Control LabUniversity of Minnesota Prof. Perry Y. LiLab 5: Relief valves ObjectiveRelief valves are the most common pressure control valves. They are used to maintain or limit the pressure at the inlet port to be at or below a pre-
Minnesota - ME - 4232
ME 4232: Fluid Power Control LabUniversity of Minnesota Prof. Perry Y. LiLab 6: Meter in / Meter out circuit ObjectiveWe saw in Labs. 3 and 4 that needle valves and PCFCs are used to control flow rate. Because of the direct relationship between flow ra
Minnesota - ME - 4232
ME 4232: Fluid Power Control LabUniversity of Minnesota Prof. Perry Y. LiLab 7: Check valves &amp; Pilot operated check valves ObjectiveCheck valves are one-way directional valves i.e., allow free-flow in one direction and block the flow in the other direc
Minnesota - ME - 4232
Fully adjustable needle valveFunctional Group: Products : Cartridges : Flow Control : 2 Port : Fully Adjustable Needle ValveCapacity: .19 in. (4,8 mm) Model: NFCC-KDNProduct Description Needle valves are fully adjustable orifices used to regulate flow.
Minnesota - ME - 4232
Fully adjustable needle valveFunctional Group: Products : Cartridges : Flow Control : 2 Port : Fully Adjustable Needle ValveCapacity: .25 in. (6,4 mm) Model: NFDC-KANProduct Description Needle valves are fully adjustable orifices used to regulate flow.
Minnesota - ME - 4232
Direct-acting relief valveFunctional Group: Products : Cartridges : Relief : 2 Port : Direct ActingCapacity: 12 gpm (45 L/min.) Model: RDBA-KANProduct Description Direct-acting relief cartridges are normally closed, pressure-limiting valves used to pro
Minnesota - ME - 4232
Direct-acting relief valveFunctional Group: Products : Cartridges : Relief : 2 Port : Direct ActingCapacity: 12 gpm (45 L/min.) Model: RDBA-LANProduct Description Direct-acting relief cartridges are normally closed, pressure-limiting valves used to pro
Minnesota - ME - 4232
Pilot operated, balanced piston relief valveFunctional Group: Products : Cartridges : Relief : 2 Port : Pilot Operated, Balanced PistonCapacity: 12 gpm (45 L/min.) Model: RPCC-KANProduct Description Pilot-operated, balanced-piston relief cartridges are
Minnesota - ME - 4232
Pilot operated, balanced piston relief valveFunctional Group: Products : Cartridges : Relief : 2 Port : Pilot Operated, Balanced PistonCapacity: 12 gpm (45 L/min.) Model: RPCC-LANProduct Description Pilot-operated, balanced-piston relief cartridges are
Minnesota - ME - 4232
Pilot operated, balanced piston sequence valveFunctional Group: Products : Cartridges : Sequence : 3-Port : Pilot Operated, Balanced PistonCapacity: 15 gpm (60 L/min.) Model: RSDC-LANProduct Description Pilot-operated, balanced piston sequence valves w
FIU - MATH - 214
CHAPTER 1Integrals1.1. Areas and Distances. The Definite Integral 1.1.1. The Area Problem. The Definite Integral. Here we try to find the area of the region S under the curve y = f (x) from a to b, where f is some continuous function.Yy=f(x)SOabX