Task 3: Analysis of the Crane System and Simulation (CLO3 and CLO4) It is important to analyse the dynamic characteristics of the gantry crane system, for design of an efficient controller to achieve the control objectives. Table 2 shows the parameters of the gantry crane. Parameters Trolley mass Payload mass, m2 Cable length, 1 Gravitational acceleration Damping coefficient Table 2: Gantry crane parameters Value (unit) Parameters 2.0 kg Resistance 0.5-3.0 kg Torque constant 0.5-3.0 m Electric constant 9.81 m/s Radius of pulley 0.01 Ns/m Gear ratio Value (unit) 2.612 0.007 Nm/A 0.007 Vs/rad 0.02 m 0.15 Write a Matlab file (m-file) to: a) Represent the transfer functions in Matlab with the system parameters. b) Find the system poles and zeros, and discuss its stability. Also plot the pole-zero map. Represent the state-space representation with the system parameters. d) Find the system poles and zeros based on the state-space matrices. Change the values of the cable length, I and the payload mass, m, and observe the effects on the poles and zeros, and stability Task 3: Analysis of the Crane System and Simulation (CLO3 and CLO4) It is important to analyse the dynamic characteristics of the gantry crane system, for design of an efficient controller to achieve the control objectives. Table 2 shows the parameters of the gantry crane. Parameters Trolley mass Payload mass, m2 Cable length, 1 Gravitational acceleration Damping coefficient Table 2: Gantry crane parameters Value (unit) Parameters 2.0 kg Resistance 0.5-3.0 kg Torque constant 0.5-3.0 m Electric constant 9.81 m/s Radius of pulley 0.01 Ns/m Gear ratio Value (unit) 2.612 0.007 Nm/A 0.007 Vs/rad 0.02 m 0.15 Write a Matlab file (m-file) to: a) Represent the transfer functions in Matlab with the system parameters. b) Find the system poles and zeros, and discuss its stability. Also plot the pole-zero map. Represent the state-space representation with the system parameters. d) Find the system poles and zeros based on the state-space matrices. Change the values of the cable length, I and the payload mass, m, and observe the effects on the poles and zeros, and stability