Posted: January 4th, 2017

Using frequency domain approach, design a lead compensator to achieve a velocity error constant no less than 35 and a step response overshoot of no greater than 20%.

Questions 1. Consider the unity feedback control system where the plant transfer function is given by: ��= � ��+2 �+40 a. Using the frequency domain approach, determine the gain K required to give an overshoot, in response to a step input, of approximately 20%. Explain how you achieved your result. [10 Marks]  b. Using frequency domain approach, design a lead compensator to achieve a velocity error constant no less than 35 and a step response overshoot of no greater than 20%. Describe each stage of your design. If performance specifications are not met first time, perform another design iteration. [15 Marks]  c. Use MATLAB to plot the response of the control system, (designed in b.), to a unit ramp, showing both system output and ramp input, and evaluate the percentage steady state error to the ramp input signal. [5 Marks] d. Use MATLAB to evaluate the performance of your final design in the time and frequency domain. Present these in tabular form – see Table 1, and provide a written conclusion for your design. [5 Marks] Quantity  Value Steady state error to a unit ramp Rise Time Settling Time Percentage Overshoot Phase Margin Gain Margin Bandwidth Peak Magnitude Resonant frequency Table 1 Page 4 of 5 ACS221 –Control Systems Design Assignment 2. A unity feedback servo system has a plant with a transfer function of: ��= � ��+2 �+30  a. Using the root locus approach, design a phase lead compensator to meet the following performance specifications:  • The settling time resulting from a step input to be less than 4s  • The overshoot is less than 15% Describe clearly each stage of your design. If performance specifications are not met first time, perform another design iteration. [15 Marks]