Three-weight elevator system with flexible rope
Assignment: Analyze the mechanical system according to the picture:
Elevator Modeling and DC Drive Speed Controller Design
Parameters (estimate, can be adjusted accordingly):
v1 = 1 m/s. m0 = 150 kg, m2 = 50 kg, b3 = 100 Ns/m
Rope: k = SE/l coefficient of elasticity of the rope
E = 2,1 109 Pa, l = 10 m- rope length , r = 10 cm- rope radius
|b| usually in the range of max. a few% of the value |k|.
For the investigation, select suitable parameters of the system at which its frequency properties (resonance, etc.) begin to manifest.
The report must contain the following outputs:
Compilation of system equations and the corresponding matrix equation:
- Finding the transfer function of the system by applying both methods in symbolic MATLAB. Specify it in (1) in symbolic form and (2) in numeric form for the selected parameter values.
- Transient characteristic of the system and the corresponding Bode AFCH. Describe their course and state which circuit it is. In the table (eg below the graph), state the values of zeros and poles.
- Investigation of the dependence of the change in the properties of the system - time responses and its frequency characteristics on each of the system parameters (usually at three frequency values, while the other parameters remain at the original values). Describe verbally the influence of individual parameters on the dynamic properties of the system.
- System model in Simulink derived from system equations (not just Transfer Function block).
- System responses from Simulink to a harmonic signal at three different frequencies chosen to capture the frequency characteristics of the system (usually in the LAFCH extreme and two other points - one at a lower and the other at a higher frequency, where there is a significant phase change or LFCH amplitude change ).
- Derivation of the state model of the system. Verify by simulation that it is the same system - compare with the results obtained in point 2.
- System simulation using Simscape. By comparing the response with those in point 2, you verify the correctness of the derived mathematical model.
- Build a GUI in MATLAB enabling convenient and fast system analysis.
Finally, thoroughly analyze the achieved results (what circuit it is, what are the used methods of solution, what are the achieved results, what is the influence of individual parameters on the change of properties, etc.).