A common application of control systems is in regulating the temperature of a chemical process The flow of a chemical reactant to a process is controlled by an actuator and valve. The reactant causes the temperature in the vat to change. This temperature is sensed and compared to a desired set-point temperature in a closed loop, where the flow of reactant is adjusted to yield the desired temperature. The transfer function of the system is as shown below: s(s+3) G(s) 52 +592 +45 +20 By using s-plane plot, show either the system is stable, marginally stable or unstable. (8 marks) Cutting forces should be kept constant during machining operations to prevent changes in spindle speeds or work position. Such changes would deteriorate the accuracy of the work's dimensions. A control system is proposed to control the cutting force. The plant is difficult to model, since the factors that affect cutting force are time varying and not easily predicted. However, assuming the simplified force control model shown in Figure Q2(c). (1) Show the closed-loop transfer function for the system of the system as below T(s) = K(s +3) s'+7s' +14s +(8+K)s +3K (2 marks) (ii) Determine the range K to keep the system stable using the Routh-Hurwitz criterion (11 marks) |