Question #1 (60 pts): As an engineer you want to design a mechatronic system that is constructed as a combination of an electromechanical subsystem and an electronics subsystem. You also desire to design a digital control closed-loop system for getting the velocity of this system to the predetermined reference level. Input and output of the electromechanical subsystem are given as torque and position, respectively, while input and output of electronics subsystem are given as current and torque, respectively. You have an accelerometer (i.e., measurement device used for measuring acceleration) and a measurement device for measuring current. Both of these devices realize the measurements continuously. Closed-loop digital control block diagram must be in a form where the torque that is able to get the velocity of the system to the reference level is determined in a digital controller, then output of this controller is used as a reference input of another digital controller where the current value is obtained according to the predetermined torque value. a) (20 pts) Realize the necessary design (i.e., design of system and controllers) that makes the whole system a Type-II system. Explain your approach clearly and verify your result mathematically. b) (10 pts) Assume that you decide to use just one digital proportional controller for controlling the system designed in (a) (i.e., instead of using two separate controllers you decided to use one controller to control the combined system). Determine the interval of the control gain of the proportional controller that guarantees the BIBO stability of this closed-loop control system. You have to use one of Jury's Stability Test or Routh's Array in accordance with Bilinear Transformation method for the solution of this part. c) (10 pts) Is it possible to obtain zero convergence of the error just by using one digital proportional controller whose control gain selection interval was determined in (b). Support your comment and show your result mathematically. d) (10 pts) Assume that you decide to use two separate digital proportional controllers for controlling the system designed in (a). Determine the interval of the control gains of the proportional controllers that guarantees the BIBO stability of this closed-loop control system. You have to use one of Jury's Stability Test or Routh's Array in accordance with Bilinear Transformation method for the solution of this part. e) (10 pts) Is it possible to obtain zero convergence of the error by using two separate digital proportional controllers whose control gains selection interval were determined in (d). Support your comment and show your result mathematically. Question #1 (60 pts): As an engineer you want to design a mechatronic system that is constructed as a combination of an electromechanical subsystem and an electronics subsystem. You also desire to design a digital control closed-loop system for getting the velocity of this system to the predetermined reference level. Input and output of the electromechanical subsystem are given as torque and position, respectively, while input and output of electronics subsystem are given as current and torque, respectively. You have an accelerometer (i.e., measurement device used for measuring acceleration) and a measurement device for measuring current. Both of these devices realize the measurements continuously. Closed-loop digital control block diagram must be in a form where the torque that is able to get the velocity of the system to the reference level is determined in a digital controller, then output of this controller is used as a reference input of another digital controller where the current value is obtained according to the predetermined torque value. a) (20 pts) Realize the necessary design (i.e., design of system and controllers) that makes the whole system a Type-II system. Explain your approach clearly and verify your result mathematically. b) (10 pts) Assume that you decide to use just one digital proportional controller for controlling the system designed in (a) (i.e., instead of using two separate controllers you decided to use one controller to control the combined system). Determine the interval of the control gain of the proportional controller that guarantees the BIBO stability of this closed-loop control system. You have to use one of Jury's Stability Test or Routh's Array in accordance with Bilinear Transformation method for the solution of this part. c) (10 pts) Is it possible to obtain zero convergence of the error just by using one digital proportional controller whose control gain selection interval was determined in (b). Support your comment and show your result mathematically. d) (10 pts) Assume that you decide to use two separate digital proportional controllers for controlling the system designed in (a). Determine the interval of the control gains of the proportional controllers that guarantees the BIBO stability of this closed-loop control system. You have to use one of Jury's Stability Test or Routh's Array in accordance with Bilinear Transformation method for the solution of this part. e) (10 pts) Is it possible to obtain zero convergence of the error by using two separate digital proportional controllers whose control gains selection interval were determined in (d). Support your comment and show your result mathematically
