TEL302 Control System- Automobile Manufacturing Factory

Task

If a process/plant, such as a mechanical system, has high-frequency vibration modes, then a desired closed-loop response may be difficult to obtain. These high-frequency vibration modes can be modeled as part of the plant’s transfer function by pairs of complex poles near the imaginary axis. In a closed-loop configuration, these poles can move closer to the imaginary axis or even cross into the right half-plane. Instability or high-frequency oscillations superimposed over the desired response can result.
One way of eliminating the high-frequency oscillations is to cascade a notch filter with the process/plant. The notch filter has zeros close to the low-damping-ratio poles of the plant as well as two real poles. Other cascade compensators can now be designed to yield a desired response.

Part 1

1. Given the following transfer function in Figure 1, determine
                                                                                         
 
Figure 1
a. The step response of the system, thus the overshoot, settling time and steady state error.
b. The root-locus plot of the system and comment the stability.
         
2. Design and apply a notch filter to achieve a better step response and stability. Compare and comment on the results of before and after the filter Id applied to the system.

Part 2

2 – Robotic Arm Simulations

Robotic arms monly used especially in the heavy industry such as automobile manufacturing factory. Along the production line, one of the robotic arm is required to have a bandwidth of at least 1 Hz and a phase margin (PM) of 45o. The system is with the process transfer function as shown below in Figure 2:
                                                                                                                       
Figure 2: Robotic arm control system.

Required Tasks

1. Determine a suitable value for the gain, K, and suggest a suitable phase compensator, Gc(s).
2. Justify your suggestion of the phase compensator.
3. Obtain the transfer function for the phase compensator by using VisSim simulator software.

Design Procedure

The general procedures for designing a phase compensator is given below:
1. Determine the gain, K, to satisfy the requirement such as the steady state error tolerance and the bandwidth needed.
2. Construct Bode plot and measure the PM. 
3. Determine the values of α and . Refer unit materials for the choice of phase compensator.
4. Calculate the frequency at which the maximum phase lead to be located, ωm.
5. Calculate the τ value. 
6. Substitute the α and τ values into the phase compensator transfer function. 
7. Redraw the Bode plot and check if the PM fulfil the requirement. If not, the procedures are repeated by appropriate adjustment to the gain, K, and phase allowance of the .

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