University study material for Control and Actuating Devices for Mechanical Systems in the Mechanical Engineering degree programme at Politecnico di Milano. The document covers: Master of Science Course in Mechanical Engineering Politecnico di Milano - Bovisa Campus CONTROL OF MECHANICAL SYSTEMS - 059180 Prof. Edoardo Sabbioni Academic Year 2025-2026 β 1st Semester EXAM SIMULATION (total time 90 min.) Name: Surname: Personal code: 1 π = 0.5 [ππ] π½ =
University study material for Control and Actuating Devices for Mechanical Systems in the Mechanical Engineering degree programme at Politecnico di Milano. The document covers: Master of Science Course in Mechanical Engineering Politecnico di Milano - Bovisa Campus CONTROL OF MECHANICAL SYSTEMS - 059180 Prof. Edoardo Sabbioni Academic Year 2025-2026 β 1st Semester EXAM SIMULATION (total time 90 min.) Name: Surname: Personal code: 1 π = 0.5 [ππ] π½ =
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Master of Science Course in Mechanical Engineering Politecnico di Milano - Bovisa Campus CONTROL OF MECHANICAL SYSTEMS - 059180 Prof. Edoardo Sabbioni Academic Year 2025-2026 β 1st Semester EXAM SIMULATION (total time 90 min.) Name: Surname: Personal code: 1
π = 0.5 [ππ] π½ = 0.25 [πππ2 ] π΅π π = π[ ] π π΅π πΌ= π[ ] πβπππ π π = 1 [π] ππ ππ = 0.001 [ ] π΄ πΏπ = 0.166 [π»] π π = 1 [πβπ] { ππ = 0.33 Consider the system represented in the figure, assuming that the disturbance d is null (d=0). Part 1 1. Write the linearized equation of motion of the system (placed in the vertical plane) considering that a force πΉ = πΌπ₯Μ acts on the mass M (according to the direction indicated in the figure). Highlight the generalized mass and damping of the system. 2. Calculate the poles of the passive system. 2
Letβs control the speed πΜ of the mass M by means of the torque T, supplied by a proportional (P) regulator. 3. Analyze the stability of the feedback control system and calculate the number of unstable poles (if any). 4. Letβs now consider dβ 0. Calculate the transfer function Ld between the speed π₯Μ of the mass M and the disturbance d and draw the Bode diagrams of Ld, highlighting the effect of the control gain Kp (assume a stable controlled system). Consider that T is provided by a permanent magnet DC motor rigidly connected to disk 1 and assume that the disturbance d is null (d=0). 5. Write the equation of motion of the electro-mechanical system. 6. Write the equation of the transfer funcion between input voltage of the motor Va and the speed of the mass M, π₯Μ . Part 2 Letβs control the speed πΜ of the mass M by means of a Proportional-Integral (PI) regulator acting on the armature voltage of the motor Va. 7. Draw the block diagram of the feedback control system. 8. Calculate the equation of the open-loop transfer funcion. 9. Analyse the stability of the system applying the Bode criterium (if possible), and the Nyquist criterion. Assume that the motor introduces a real negative pole at high frequency (P=-6), which only slightly modifies the position of the poles of the passive system. 10. Plot a qualitative root locus of the feedback control system. Assume that the motor introduces a real negative pole at high frequency (P=-6), which only slightly modifies the position of the poles of the passive system. 11. Write the eqation of motion of the feedback control system using the state- space form. 3
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