![Hybrid vehicle. FIGURE P1 shows the block diagram of a possible cascade control scheme for an<br>HEV driven by a dc motor (Preitl, 2007).<br>The block diagram of the speed control of an HEV taken from FIGURE P1, and rearranged as a<br>unity feedback system is shown in FIGURE P2. Here the system output is C(s) = Kss V(s), the output<br>voltage of the speed sensor/transducer.<br>pC, Av,-<br>Speed K, Gre(s)<br>controller command<br>Torque Amplifier<br>controller output<br>& power voltage<br>amplifier<br>Acro-<br>Motive dynamie<br>Armature<br>Speed<br>|drag torque<br>Angular<br>speed,<br>Ref.<br>circuit Armature<br>torque<br>Vehicle<br>signal<br>R,(s).<br>error<br>U(s)<br>T(s)T,(s)<br>current<br>E,(s)<br>speed, V(s)<br>Gse(s)<br>K, Grc(s)<br>R.<br>tot<br>Friction<br>Feedback<br>speed signal<br>Kss2(s)<br>Feedback<br>torque<br>current signal<br>Kes I(S)<br>T,(s)<br>E,(s)<br>Back emf<br>D=k<br>ks<br>Current sensor<br>sensitivity<br>Kcs<br>Speed sensor<br>sensitivity<br>Kss<br>FIGURE P1 Hybrid Vehicle<br>R (s),<br>E (s)<br>Uc(s)<br>|C(s)<br>+<br>Gsc(s)<br>0.11 (s + 0.6)<br>SC<br>s (s + 0.5173) + 5 (s + 0.6) (s + 0.01908)<br>URE P2 Block diagram of the speed control of an HEV<br>a. Assume the speed controller is given as Gsc(s) = Kpsc . Find the gain, Kpsc , that yields a<br>steady-state error, estep(∞) = 1%. Show your calculations, Simulink work and the results.<br>b. Now assume that in order to reduce the steady-state error for step inputs, integration is added<br>to the controller yielding Gsc(s) = Kpsc +(K1sc/s)=100+(K1sc/s) Find the value of the integral<br>gain, Kısc , that results in asteady-state error, eramp( 0)=2.5%. Show your calculations,<br>%3D<br>Simulink work and the results.<br>c. Design an active controller [new Gsc(s)] such that the system can operate with a settling time<br>of 4 seconds and less than 5% overshoot and with zero steady-state error for a step input.<br>Show your calculations, Simulink work and the results (draw the root locus of compensated<br>and uncompensated system).<br>](https://s3.us-east-1.amazonaws.com/storage.unifolks.com/qimg-008/008_amekzp0-4mwdejid.jpeg)
Extracted text: Hybrid vehicle. FIGURE P1 shows the block diagram of a possible cascade control scheme for an HEV driven by a dc motor (Preitl, 2007). The block diagram of the speed control of an HEV taken from FIGURE P1, and rearranged as a unity feedback system is shown in FIGURE P2. Here the system output is C(s) = Kss V(s), the output voltage of the speed sensor/transducer. pC, Av,- Speed K, Gre(s) controller command Torque Amplifier controller output & power voltage amplifier Acro- Motive dynamie Armature Speed |drag torque Angular speed, Ref. circuit Armature torque Vehicle signal R,(s). error U(s) T(s)T,(s) current E,(s) speed, V(s) Gse(s) K, Grc(s) R. tot Friction Feedback speed signal Kss2(s) Feedback torque current signal Kes I(S) T,(s) E,(s) Back emf D=k ks Current sensor sensitivity Kcs Speed sensor sensitivity Kss FIGURE P1 Hybrid Vehicle R (s), E (s) Uc(s) |C(s) + Gsc(s) 0.11 (s + 0.6) SC s (s + 0.5173) + 5 (s + 0.6) (s + 0.01908) URE P2 Block diagram of the speed control of an HEV a. Assume the speed controller is given as Gsc(s) = Kpsc . Find the gain, Kpsc , that yields a steady-state error, estep(∞) = 1%. Show your calculations, Simulink work and the results. b. Now assume that in order to reduce the steady-state error for step inputs, integration is added to the controller yielding Gsc(s) = Kpsc +(K1sc/s)=100+(K1sc/s) Find the value of the integral gain, Kısc , that results in asteady-state error, eramp( 0)=2.5%. Show your calculations, %3D Simulink work and the results. c. Design an active controller [new Gsc(s)] such that the system can operate with a settling time of 4 seconds and less than 5% overshoot and with zero steady-state error for a step input. Show your calculations, Simulink work and the results (draw the root locus of compensated and uncompensated system).