Hi i need help with part d, thank you.

CN4227R Advanced Process Control Project Parts (a) and (b) due on 8 March Parts (c) and (d) due on 16 April The enhanced control (EC) system depicted in Figure 1 consists of the process G(s), PID/PI controller C(s) and process model M(s). The model M(s) is factorized as follows M(s)=M1(s)M2(s) (a)For a process with time delay, G(s)=G0(s)e where G0(s) is the process model without time delay, how is M(s) factorized in order for the EC to yield identical closedloop transfer fnction for set-point change to that obtained by the Smith Predictor under perfect model condtion, i.e., G(s)=M(s) ? Lastly, is feedback controller C(s) designed based on M(s) or other dynamics.in Figure 1? (b)To confirm the result in part (a), process model and PI controller used in the page 43 of the Lecture Note on model-based design are considered. Specifically, two Simulink files for Smith predictor and EC in Figure 1 are required for this comparative study. In addition, the set-point responses of Smith predictor and feedback controller given in Slide 43 are duplicated and included in your report. Lastly, explain and discuss whether the response of the EC is identical to that of the Smith predictor and is this comparative result consistent with the conclusion drawn from part (a)? (c)Under perfect model condition, explain why the EC with appropriate factorization of process model, G(s)=M(s)=(s+a)M(s), is capable of giving faster and aggressive closed-loop response compared with the classical feedback (FB) control system when these two control systems are used to control an inverse dynamics in the absence of time delay? To be specific, is M(s) in Figure 1 factorized by Seborg or Morari formula in this case? In order to explain faster performance of the EC, Bode stability analysis results of the EC and FB can be compared, by which the performance difference of these two control systems can be inferred. Since controller is not available, the same controller is employed for the EC and FB for the ease of analysis and comparison of Bode stability results. (d)To verify the result in part (c), consider the process given in Eq. 2. To design two PID controllers in FB and EC control systems, appropriate IMC-based PID formulas given in the IMC table are used. Next, for a unit step change in the set-point, two IMC filter time constants in the two control systems are tuned to achieve their respective best servo responses using IAE as a performance metric (a Simulink file will be uploaded to demonstrate how to calculate IAE). Lastly, explain and justify whether the best achievable performance attained by the EC outperforms that obtained by the FB, which is discussed to be the case in a more generic setting in part (c). In general, a smaller IMC filter time constant results in larger controller gain and u faster closed-loop response. However, a very aggressive controller gives an excessive oscillation and hence is not considered in practice. Therefore, if controller gain diverges as IMC filter time constant approaches to zero, a lower bound of 0.09 or 0.1 instead of 0 is imposed and chosen as the valid range used in simulation studies in this project. To determine the optimal value of IMC filter time constant, a plot or table of IAE vs IMC filter time constant should be provided. Additionally, one plot displaying the set-point change responses for three different IMC filter tunings is needed for each control system. Lastly, one figure showing the best set-point change responses of these two control systems is required as well. G(s)=3(2s+1)(4s+1)s+1 Note that the relevant calculations and figures/tables should be provided to support your discussions in the report. Note * In Simulink, PID controller with the following equation, P+I/s+Ds, is used. As a result, the following relations hold, P=Kc,I=Kc/I and D=KcD, where Kc,I, and D are the PID parameters defined in the textbook and lecture notes. CN4227R Advanced Process Control Project Parts (a) and (b) due on 8 March Parts (c) and (d) due on 16 April The enhanced control (EC) system depicted in Figure 1 consists of the process G(s), PID/PI controller C(s) and process model M(s). The model M(s) is factorized as follows M(s)=M1(s)M2(s) (a)For a process with time delay, G(s)=G0(s)e where G0(s) is the process model without time delay, how is M(s) factorized in order for the EC to yield identical closedloop transfer fnction for set-point change to that obtained by the Smith Predictor under perfect model condtion, i.e., G(s)=M(s) ? Lastly, is feedback controller C(s) designed based on M(s) or other dynamics.in Figure 1? (b)To confirm the result in part (a), process model and PI controller used in the page 43 of the Lecture Note on model-based design are considered. Specifically, two Simulink files for Smith predictor and EC in Figure 1 are required for this comparative study. In addition, the set-point responses of Smith predictor and feedback controller given in Slide 43 are duplicated and included in your report. Lastly, explain and discuss whether the response of the EC is identical to that of the Smith predictor and is this comparative result consistent with the conclusion drawn from part (a)? (c)Under perfect model condition, explain why the EC with appropriate factorization of process model, G(s)=M(s)=(s+a)M(s), is capable of giving faster and aggressive closed-loop response compared with the classical feedback (FB) control system when these two control systems are used to control an inverse dynamics in the absence of time delay? To be specific, is M(s) in Figure 1 factorized by Seborg or Morari formula in this case? In order to explain faster performance of the EC, Bode stability analysis results of the EC and FB can be compared, by which the performance difference of these two control systems can be inferred. Since controller is not available, the same controller is employed for the EC and FB for the ease of analysis and comparison of Bode stability results. (d)To verify the result in part (c), consider the process given in Eq. 2. To design two PID controllers in FB and EC control systems, appropriate IMC-based PID formulas given in the IMC table are used. Next, for a unit step change in the set-point, two IMC filter time constants in the two control systems are tuned to achieve their respective best servo responses using IAE as a performance metric (a Simulink file will be uploaded to demonstrate how to calculate IAE). Lastly, explain and justify whether the best achievable performance attained by the EC outperforms that obtained by the FB, which is discussed to be the case in a more generic setting in part (c). In general, a smaller IMC filter time constant results in larger controller gain and u faster closed-loop response. However, a very aggressive controller gives an excessive oscillation and hence is not considered in practice. Therefore, if controller gain diverges as IMC filter time constant approaches to zero, a lower bound of 0.09 or 0.1 instead of 0 is imposed and chosen as the valid range used in simulation studies in this project. To determine the optimal value of IMC filter time constant, a plot or table of IAE vs IMC filter time constant should be provided. Additionally, one plot displaying the set-point change responses for three different IMC filter tunings is needed for each control system. Lastly, one figure showing the best set-point change responses of these two control systems is required as well. G(s)=3(2s+1)(4s+1)s+1 Note that the relevant calculations and figures/tables should be provided to support your discussions in the report. Note * In Simulink, PID controller with the following equation, P+I/s+Ds, is used. As a result, the following relations hold, P=Kc,I=Kc/I and D=KcD, where Kc,I, and D are the PID parameters defined in the textbook and lecture notes