Question 1: The error in a feedback control system is central. Feedback control algorithms use the error in order to calculate the action to be done. What is the definition of error in a feedback control system: A- The difference between the set-point and the measured process variable B- The difference between the disturbance and the measured process variable C- The disturbance D- The measurement error Question 2: The amount of excess air in the flue gas leaving a boiler has a direct impact on boiler efficiency and the cost of steam generation. The control system's objective is to maintain the amount of excess air as close as possible to the set-point. The result is that the error (actual excess air value minus set-point value) has the form of a sine wave as depicted in the figure. This results in the same sine wave form of profit loss. The amplitude of the sine wave of loss is proportional to that of the sine wave of the error. If we reduce the amplitude of the sine wave of the error by half, what would be the impact on the profit loss? The new profit loss will be: A- 0.5 x Old profit loss B- 0.25 x Old profit loss C- 0.75 Old profit loss D- (1 / π) x Old profit loss Hint: the average amplitude of a sinusoidal signal is proportional to the amplitude of that signal Question 3: We have two first order processes. If we organize the processes such as the output of the first process is the input of the second. The resulting process that corresponds to the two processes organized in series as mentioned, is: A- An unstable process B- A second order process C- A first order process D- A high gain process Question 4: What is the equivalent transfer function of the following: A- Y(s)/R(s) = (G1G2G5 - G1G6)/(1 - G1G3 + G1G2G4) B- Y(s)/R(s) = (G1G2G5 + G1G6)/(1 + 2G1G3 + G1G2G4) C- Y(s)/R(s) = (G1G2G5 + G1G6)/(1 + G1G3 - G1G2G4) D- Y(s)/R(s) = (G1G2G5 + G1G6)/(1 - G1G3 + G1G2G4) Question 5: Consider the following step responses of a second order process. Each curve A, B, C corresponds to a step response for a damping ration ξ. Which statement is correct: A- A corresponds to ξ< 1, B corresponds to ξ = 1 and C corresponds to ξ > 1 B- A corresponds to ξ= 1, B corresponds to ξ < 1 and C corresponds to ξ > 1 C- A corresponds to ξ> 1, B corresponds to ξ = 1 and C corresponds to ξ < 1 D- A corresponds to ξ< 1, B corresponds to ξ > 1 and C corresponds to ξ = 1 Question 6: Consider two MIMO control systems that are connected. y1 denotes the output of the first system, u1 denotes the input of the first system, y2 denotes the output of the second system, u2 denotes the input of the second system. If y denotes the output of the equivalent system and u denotes the input of the equivalent system, then the connection is as follows: y = y1 + y2; u = u1 = u2; What is the transfer matrix form of the equivalent system: A- y(s) = G2(s)G1(s)u(s) B- y(s) = (G2(s)+G1(s))u(s) C- y(s) = (I + G2(s)G1(s))u(s) D- y(s) = (I + G2(s)G1(s))-1u(s) Question 7: Consider the following disturbance signals: 1- Constant signal of the form y(t) = a1 , where a1 is a constant 2- Ramp signal of the form y(t) = a1 + a2t, where a1, a2 are constants 3- Measurement noise 4- Internal noise Which statement is the correct one: A- All signals are considered stochastic disturbance B- All signals are considered deterministic disturbance C- Signals 1- and 2- are considered deterministic disturbance and signals 3- and 4- are considered stochastic disturbance D- Signals 3- and 4- are considered deterministic disturbance and signals 1- and 2- are considered stochastic disturbance Question 8: Consider a MIMO process where each input influences only one output. Which of the following statements is correct: A- We can decouple the process into multiple SISO sub-processes and tune each one independently B- We cannot tune each sub-process independently C- We can only use matrix operation to tune the MIMO process D- We can average the inputs to obtain one input and do the same with the outputs to obtain one output. The MIMO process can then be considered a SISO process and can be tuned accordingly. Question 9: Consider the following Relative Gain Array Which of the following statements is correct: A- The best pairing is Y1->U1, Y2->U2, Y3->U3 B- The best pairing is Y1->U2, Y2->U1, Y3->U3 C- The best pairing is Y1->U1, Y2->U3, Y3->U2 D- The best pairing is Y1->U3, Y2->U1, Y3->U2 Question 10: Consider the following Gain array that we want to decouple using Singular Value Decomposition (SVD) Question 11: We are using an Analog to Digital Converter to convert an analog Voltage signal into a digital one. The quantiser uses 8 bits and has a full scale of 10 V. What would be the output of the quantiser if the input is 9.75V: A- 11111100 B- 0011 C- 10101001 D- 11111010 Question 12: Consider two discretised processes connected in series. B(z) and C(z) denote the transfer functions in the z domain for the first and second process respectively. What is the equivalent transfer function E(z) of the two processes: A- E(z) = B(z).C(z) B- E(z) = B(z) + C(z) C- E(z) = B(z).C-1(z) D- E(z) = B(z) - C(z) A- X(z)= z B- X(z)= 1 C- X(z)= e-z D- X(z)= 0