Tasks (100 marks total] - complete the following tasks: 1) For the case of the input being a unit step (eg. Ry(s) = 1/s), obtain an expression for the output Laplace function Ci(s). [5 marks] 2) For the case of the input being a unit ramp (eg. Ro(s) = 1/s), obtain an expression for the output Laplace function C(s). [5 marks] 3) Apply the final value theorem for the two given cases to obtain (individually) a steady-state input value and a steady-state output value. That is, obtain (0) and coo) for the system subjected to unit step input, and also for unit ramp input. [5 marks] 4) Using the results of Task #3. attempt to obtain the expected steady-state error for both of the given cases (ie. unit step and unit ramp conditions) based on the definition of the steady-state error. Note: You will likely encounter an issue with the value of your obtained value of steady-state error for one of the cases. For example, the case of roo) and c(oc) both being infinite is an issue - where the difference between two infinite "values' does not necessarily amount to zero. For such a case, you should use the steady-state error method that involves finding the relevant static error constant (eg. K) - followed by using an error formula (eg, involving K.) for calculating the steady-state error. [10 marks] 5) Use Simulink to model the system for the case of a unit step input. Present scope plots showing the input and the output time response (overlaid in a single scope image). A Simulink multiplexer block will be needed in conjunction with the scope to plot both input and output versus time, simultaneously) You may need to estimate the 2% serrling time of the system, which can be used for choosing a suitable time span for your plots. Your plot will start at t=0 and then end at the time of your own choosing. The span needs to be chosen appropriately - so that the dynamics' in the output curve (versus time) can be seen clearly for both the step response [20 marks] the dynamics' in the output curve (versus time) can be seen clearly for both the step response. [20 marks] 6) Repeat task #5 for the case of a unit ramp input. [20 marks) 7) Make use of the 'multiplexer' block (in Simulink) and "scope' block, and a difference' block (based on a re-configured summation block) to plot the "error versus time" e(t) curves for both the unit step and unit ramp cases. The difference block will allow you to plot r(t) - c(t), which is e(t). Your error-versus-time plot will start at t = 0 and then end at a time of your own choosing. The span must be chosen appropriately - so that the dynamics in the error curve (versus time) can clearly be seen. That is, choose a time span for the plot that allows readers to see quite clearly see the variation of error as time increases (starting from t=0). [25 marks) 8) Estimate the values e) from your observations of the e(t) plots (via the scope plots of Simulink). The estimates are expected to align with the values predicted from EE3600 - Automatic Control 2 Task #4. Please confirm that the estimated steady state error (from the simulations) align with the predicted values. [10 marks] o DELL F2 F3 X F4 1 F5 F6 E7 F8 F9 F10 # $ % A & * 2 3 4 5 6 7 Tasks (100 marks total] - complete the following tasks: 1) For the case of the input being a unit step (eg. Ry(s) = 1/s), obtain an expression for the output Laplace function Ci(s). [5 marks] 2) For the case of the input being a unit ramp (eg. Ro(s) = 1/s), obtain an expression for the output Laplace function C(s). [5 marks] 3) Apply the final value theorem for the two given cases to obtain (individually) a steady-state input value and a steady-state output value. That is, obtain (0) and coo) for the system subjected to unit step input, and also for unit ramp input. [5 marks] 4) Using the results of Task #3. attempt to obtain the expected steady-state error for both of the given cases (ie. unit step and unit ramp conditions) based on the definition of the steady-state error. Note: You will likely encounter an issue with the value of your obtained value of steady-state error for one of the cases. For example, the case of roo) and c(oc) both being infinite is an issue - where the difference between two infinite "values' does not necessarily amount to zero. For such a case, you should use the steady-state error method that involves finding the relevant static error constant (eg. K) - followed by using an error formula (eg, involving K.) for calculating the steady-state error. [10 marks] 5) Use Simulink to model the system for the case of a unit step input. Present scope plots showing the input and the output time response (overlaid in a single scope image). A Simulink multiplexer block will be needed in conjunction with the scope to plot both input and output versus time, simultaneously) You may need to estimate the 2% serrling time of the system, which can be used for choosing a suitable time span for your plots. Your plot will start at t=0 and then end at the time of your own choosing. The span needs to be chosen appropriately - so that the dynamics' in the output curve (versus time) can be seen clearly for both the step response [20 marks] the dynamics' in the output curve (versus time) can be seen clearly for both the step response. [20 marks] 6) Repeat task #5 for the case of a unit ramp input. [20 marks) 7) Make use of the 'multiplexer' block (in Simulink) and "scope' block, and a difference' block (based on a re-configured summation block) to plot the "error versus time" e(t) curves for both the unit step and unit ramp cases. The difference block will allow you to plot r(t) - c(t), which is e(t). Your error-versus-time plot will start at t = 0 and then end at a time of your own choosing. The span must be chosen appropriately - so that the dynamics in the error curve (versus time) can clearly be seen. That is, choose a time span for the plot that allows readers to see quite clearly see the variation of error as time increases (starting from t=0). [25 marks) 8) Estimate the values e) from your observations of the e(t) plots (via the scope plots of Simulink). The estimates are expected to align with the values predicted from EE3600 - Automatic Control 2 Task #4. Please confirm that the estimated steady state error (from the simulations) align with the predicted values. [10 marks] o DELL F2 F3 X F4 1 F5 F6 E7 F8 F9 F10 # $ % A & * 2 3 4 5 6 7