Project 4 — Control Systems Assignment

Added on - 30 Oct 2019

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Question 1 – Stunt ControlDeveloping a suitable P, PI, PD and PID controller in MATLAB and demonstratingthe robustness of the systems with simulations of various scenarios and conditions. Theproject involve traction controls which are broadly used control systems in automotiveapplications for increasing safety and stability of a motorbike. The control systems includesESP electronic stability programs used in ICV (internal combustion-engine vehicle), ASR(anti_Slip regulations) and ABS (antilock brake systems)[ CITATION Pas08 \l 1033 ].Deriving the transfer function of the motorbike. Consider figure 1.0 below:[ CITATION ROB09 \l 1033 ]Figure A: Diagrammatic representation of the motorcycleThe dynamics of a moving motorbike is given by the following equation 1:ḧφ=[(1sin(φ))σv2+b(̈ψ+̇v(σ̇φv))]cos(φ)..............1Where v is the forward velocity of the motorbike. The yaw rate and the curvature arelinked in equation 2 below:ḧφ=gsin(φ)tan(δ)(v2ω+ḃvω+tan(φ)(vbω̇φhv2ω2))bv̇δwcos2(δ).............2Equation 2 can be linearized to form equation 3 below:Hφδ(s)=bvωh(s+vbs2gh)..............3
MATLAB design resultsContentsdesign of the motorbike transfer functiondesign of PROPOSANAL CONTROLLERdesign of PROPOSANAL-INTEGRAL (PI) CONTROLLERdesign of PROPOSANAL-DERIVATIVE (PD) CONTROLLERdesign of PROPOSANAL-INTEGRAL-DERIVATIVE (PID) CONTROLLERDesign of the motorbike transfer functionP =(25*(s + 1000))/(s^2 - 981/80)design of PROPOSANAL CONTROLLER2000 K (s + 1000)----------------------------------280 s + 2000 K s + 2000000 K - 981X1 =RiseTime: 0.3097SettlingTime: 3.8523SettlingMin: 3.9306e-004SettlingMax: 7.1900e-004Overshoot: 43.8726Undershoot: 0Peak: 7.1900e-004PeakTime: 0.8213
design of PROPOSANAL-INTEGRAL (PI) CONTROLLERThe Closed Loop Transfer Function given a PI controller is(2000 K (Ti s + 1) (s + 1000)) /3(2000000 K + 2000 K s - 981 Ti s + 80 Ti s +22000000 K Ti s + 2000 K Ti s )X2 =RiseTime: 36.4797SettlingTime: 65.1725SettlingMin: 0.8141SettlingMax: 0.8996Overshoot: 0Undershoot: 0Peak: 0.8996PeakTime: 129.8356