As an engineer you want to design a mechatronic system that is constructed as a combination of a second order electromechanical subsystem and a first order 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. 

a) Design the given system (i.e., construct the system's model and select its model parameters appropriately according to the given information) and the necessary digital controller for obtaining the zero convergence of the error for a reference velocity given as 

r(t) = t[u(t) - u(t – 3)] + 2u(t – 5)

where u(t) denotes the unit step signal. At this point it should be noted that all of the system parameters, controller's structure, sampling time and the other necessary parameters and components must be selected by you. However, you have to use at least one of the measurement devices given in the question and you cannot use any additional measurement devices. You have to explain your approach clearly, verify your result mathematically and sketch the block diagram of the control process. 

b) Assume that you decide to use a digital proportional controller for controlling the system designed in (a). 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)  Is it possible to obtain zero convergence of the error just by using a digital proportional controller whose control gain selection interval was determined in (b). Support your comment and show your result mathematically.