Assignment 3.pdf - UBC Mechanical Engineering

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(b) (c) Using the linear graph derive a state model for this system. The input is the motor magnetic torque T m and the output is the angular speed ω r of the robot arm. What is the order of the system? Discuss the validity of various assumptions made in arriving at this simplified model for a commercial robotic manipulator. T m k J m ω m ω r J r (viscous) b m Motor 1: r Gear Box (Light) Robot Arm Figure P4.7 A model of a single-degree-of-freedom robot. Problem 8 (Problem 4.8 from Textbook) Consider the rotatory feedback control system shown schematically by Figure P4.8(a). The load has inertia J, stiffness K and equivalent viscous damping B as shown. The armature circuit for the dc fixed field motor is shown in Figure P4.8(b). (a) DC Motor K v , K T T m v Power r v a v m Amplifier - K a J B K Load Torque T l Tachometer K t Gear Ratio r
(b) i R L v m v b ω = θ Figure P4.8 (a) A rotatory electromechanical system. (b) The armature circuit. The following relations are known: The back e.m.f. vB = KVω The motor torque Tm = Ki T (a) Identify the system inputs. (b) Sketch a linear graph for the system, and using that obtain a state-space model for the system. Problem 9 (Problem 4.9 from Textbook) (a) What is the main physical reason for oscillatory behaviour in a purely fluid system? Why do purely fluid systems with large tanks connected by small-diameter pipes rarely exhibit an oscillatory response? (b) Two large tanks connected by a thin horizontal pipe at the bottom level are shown in Figure P4.9(a). Tank 1 receives an inflow of liquid at the volume rate Q i when the inlet valve is open. Tank 2 has an outlet valve, which has a fluid flow resistance of R o and a flow rate of Q o when opened. The connecting pipe also has a valve, and when opened, the combined fluid flow resistance of the valve and the thin pipe is R p . The following parameters and variables are defined: C 1 , C 2 = fluid (gravity head) capacitances of tanks 1 and 2 ρ = mass density of the fluid g = acceleration due to gravity P 1 , P 2 = pressure at the bottom of tanks 1 and 2 P 0 = ambient pressure. Sketch a linear graph for the system. Using P 10 = P 1 – P 0 and P 20 = P 2 – P 0 as the state variables and the liquid levels H 1 and H 2 in the two tanks as the output variables, derive a complete, linear, state-space model for the system, systematically from the linear graph. (c) Suppose that the two tanks are as in Figure P4.9(b). Here Tank 1 has an outlet valve at its bottom whose resistance is R t and the volume flow rate is Q t when open. This flow directly
Page 1 and 2: MECH 529 DYNAMIC SYSTEM MODELING As
Page 3 and 4: through and the voltages across the
Page 5: (d) What is the number of unknown v
Page 9 and 10: Problem 10 (Problem 4.10 from Textb
Page 11 and 12: otates at an angular speed ω m ) g

Assignment 3.pdf - UBC Mechanical Engineering

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