Designing a medication delivery system to treat COVID-19 patients (continuation)
(Note: this problem does not represent an accurate description of how SARS-CoV-2 works nor how it can be accurately modelled or treated. This is merely an exercise to evaluate concepts on Signals, Systems & Controls.)
State space to Transfer function
A group of researchers have done an independent investigation and found that the SARS-CoV-2 model, for a particular gender and age group, can be described as:
(*Note: this is not an answer to COVID-Q2; use this equations to solve COVID-Q3-Q4)
(COVID-Q3) What formula do you use to find the transfer function G(s)=Y(s)/U(s)from the state space representation? Please report the formula and the specific transfer function for the state space representation above. [5 points]
(COVID-Q4) Find the gain, poles and zeros of G(s)obtained in COVID-Q3. [2 points]
Controller design in frequency domain
Researchers at UQ have developed a potential novel medication. However, this medication is expensive, and the side effects are still unknown. Therefore, they have teamed up with engineers to develop a device that can deliver just the right amount of medication, assuming that the patient can be continuously monitored. The devices control principle can be seen as a feedback controller as shown in the picture below.
(COVID-Q5) Assume that D(s) is a proportional controller with gain K. Is the system stable for all K>0? Justify your answer. [3 points] [Extra 2 points if you derive a precise range of K for which the system is stable]
--------------------------------------------------------------------------------------------------------------------------------------------------------
A smart engineer designs an initial guess for a compensator D(s) in this form:
(*Note: use this equation to solve COVID-Q6-Q8)
(COVID-Q6) Sketch the Bode plot of the open-loop transfer function when K=1, and find the cross over frequency (approximations are acceptable, but you need to justify your assumptions). [5 points]
(COVID-Q7) If you were to approximate the closed-loop system as a second order system (at K=1), derive the damping ratio, undamped natural frequency, and damped frequency. [5 points] (COVID-Q8) You are required to select a value of K, so that the closed-loop system is overdamped and has a settling time of approximately 80 days. Justify your design process. [10 points]
Discrete equivalent controller
For practical reasons, a COVID-19 patient cannot be monitored nor the medication can be adjusted continuously. Therefore, the analogue compensator found in (COVID-Q8) must be discretised.
(COVID-Q9) Determine a reasonable range of sampling period T (in days). Justify your answer. [5 points]
(COVID-Q10) Use Tustins method and T=5 days to find a discrete equivalent to D(s). [5 points]
Congratulations! Your design will now be tested by the medical device engineering testing team. As in any medical device development, the team expects that you have documented your design process, otherwise this will add significant delays in the medical device certification process! 
Designing a medication delivery system to treat COVID-19 patients (continuation) (Note: this problem does not represent an accurate description of how SARS-CoV-2 works nor how it can be accurately modelled or treated. This is merely an exercise to evaluate concepts on Signals, Systems & Controls.) State space to Transfer function A group of researchers have done an independent investigation and found that the SARS-CoV-2 model, for a particular gender and age group, can be described as: 0 -0.003\/ 0.06 -0.18 0.003 0 120 -1.8 -0.08 (3)-(.* :)) y = ( 00 1) (*Note: this is not an answer to COVID-Q2; use this equations to solve COVID-Q3-04) (COVID-Q3) What formula do you use to find the transfer function (3)=Y(3)/U(9)from the state space representation? Please report the formula and the specific transfer function for the state space representation above. [5 points) (COVID-24) Find the gain, poles and zeros of G(a)obtained in COVID-Q3. [2 points) Controller design in frequency domain Researchers at UQ have developed a potential novel medication. However, this medication is expensive, and the side effects are still unknown. Therefore, they have teamed up with engineers to develop a device that can deliver just the right amount of medication, assuming that the patient can be continuously monitored. The device's control principle can be seen as a feedback controller as shown in the picture below. Medication delivery device Desired number of free virus in the bloodstream US) SARS-CoV-2 model Y(s) Number of free virus in the bloodstream G(s) D(S) (COVID-25) Assume that D(3) is a proportional controller with gain K. Is the system stable for all K>0? Justify your answer. 13 points) [Extra 2 points if you derive a precise range of K for which the system is stable] A smart engineer designs an initial guess for a compensator D(s) in this form: -K(52 +0.0564s + 0.0093) D(S) s(s+ 0.02) (*Note: use this equation to solve COVID-26-28) (COVID-Q6) Sketch the Bode plot of the open-loop transfer function when K=1, and find the cross over frequency (approximations are acceptable, but you need to justify your assumptions) [5 points) (COVID-Q7) If you were to approximate the closed-loop system as a second order system (at K=1), derive the damping ratio, undamped natural frequency, and damped frequency. [5 points) (COVID-Q8) You are required to select a value of K, so that the closed-loop system is overdamped and has a settling time of approximately 80 days. Justify your design process. 110 points) Discrete equivalent controller For practical reas a COVID-19 discretised. be monitored nor the medication can be adjusted continuously. Therefore, the analogue found in (COVID-Q8) must be (COVID-29) Determine a reasonable range of sampling period T (in days). Justify your answer. i5 points] (COVID-Q10) Use Tustin's method and T-5 days to find a discrete equivalent to D(). is points) Designing a medication delivery system to treat COVID-19 patients (continuation) (Note: this problem does not represent an accurate description of how SARS-CoV-2 works nor how it can be accurately modelled or treated. This is merely an exercise to evaluate concepts on Signals, Systems & Controls.) State space to Transfer function A group of researchers have done an independent investigation and found that the SARS-CoV-2 model, for a particular gender and age group, can be described as: 0 -0.003\/ 0.06 -0.18 0.003 0 120 -1.8 -0.08 (3)-(.* :)) y = ( 00 1) (*Note: this is not an answer to COVID-Q2; use this equations to solve COVID-Q3-04) (COVID-Q3) What formula do you use to find the transfer function (3)=Y(3)/U(9)from the state space representation? Please report the formula and the specific transfer function for the state space representation above. [5 points) (COVID-24) Find the gain, poles and zeros of G(a)obtained in COVID-Q3. [2 points) Controller design in frequency domain Researchers at UQ have developed a potential novel medication. However, this medication is expensive, and the side effects are still unknown. Therefore, they have teamed up with engineers to develop a device that can deliver just the right amount of medication, assuming that the patient can be continuously monitored. The device's control principle can be seen as a feedback controller as shown in the picture below. Medication delivery device Desired number of free virus in the bloodstream US) SARS-CoV-2 model Y(s) Number of free virus in the bloodstream G(s) D(S) (COVID-25) Assume that D(3) is a proportional controller with gain K. Is the system stable for all K>0? Justify your answer. 13 points) [Extra 2 points if you derive a precise range of K for which the system is stable] A smart engineer designs an initial guess for a compensator D(s) in this form: -K(52 +0.0564s + 0.0093) D(S) s(s+ 0.02) (*Note: use this equation to solve COVID-26-28) (COVID-Q6) Sketch the Bode plot of the open-loop transfer function when K=1, and find the cross over frequency (approximations are acceptable, but you need to justify your assumptions) [5 points) (COVID-Q7) If you were to approximate the closed-loop system as a second order system (at K=1), derive the damping ratio, undamped natural frequency, and damped frequency. [5 points) (COVID-Q8) You are required to select a value of K, so that the closed-loop system is overdamped and has a settling time of approximately 80 days. Justify your design process. 110 points) Discrete equivalent controller For practical reas a COVID-19 discretised. be monitored nor the medication can be adjusted continuously. Therefore, the analogue found in (COVID-Q8) must be (COVID-29) Determine a reasonable range of sampling period T (in days). Justify your answer. i5 points] (COVID-Q10) Use Tustin's method and T-5 days to find a discrete equivalent to D(). is points)
