Difference between revisions of "Solutions"

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=== {{chlink|System Modeling}} ===
 
=== {{chlink|System Modeling}} ===
 
{{exercise table begin}}
 
{{exercise table begin}}
 +
{{exitem|di=|ex=1|ti=Chain of integrators form|fi=chainofint.tex|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=2|ti=Inverted pendulum|fi=balance-bal2inv.tex|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=3|ti=Disrete-time dynamics|fi=discrete-solutions.tex|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=4|ti=Keynesian economics|fi=discrete-keynes.tex|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=5|ti=Least squares system identification|fi=sysid-leastsq.tex|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=6|ti=Normalized oscillator dynamics|fi=oscillator.tex|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=7|ti=Electric generator|fi=powergrid.tex|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=8|ti=Admission control for a queue|fi=queue-admcontrol.tex|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=9|ti=Biological switch|fi=biocircuits-switchmod.tex|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=10|ti=Motor drive|fi=dcmotor-modeling.tex|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=11|ti=Uncertainty lemon|fi=lemon.tex|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=12|ti=Frequency response|fi=freqresp.tex|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=13|ti=Eye and head motion|fi=occular-blockdiag.tex|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=14|ti=Second-order system identification|fi=sysid-logdec.tex|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=15|ti=Insect vision|fi=flyvision.tex|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=16|ti=State space model for balance systems|fi=balance-statespace.tex|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=17|ti=|fi=fingerflame.tex|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=18|ti=Consensus and invariants|fi=compsys-invariants.tex|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=19|ti=Electric motor|fi=electricmotor.tex|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=20|ti=|fi=exothermic.tex|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=21|ti=|fi=caffeine.tex|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=22|ti=|fi=ballbeam-modeling.tex|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=23|ti=|fi=pvtol2invpend.tex|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=24|ti=|fi=flyflight.tex|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=25|ti=|fi=pendulum.tex|st=P|au=|co=|re=}}
 
{{exercise table end}}
 
{{exercise table end}}
  
 
=== {{chlink|Examples}} ===
 
=== {{chlink|Examples}} ===
 
{{exercise table begin}}
 
{{exercise table begin}}
 +
{{exitem|di=|ex=1|ti=Cruise control|fi=cruise-hillsim.tex|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=2|ti=Bicycle dynamics|fi=bicycle-statespace.tex|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=3|ti=Bicycle steering|fi=bicycle-steering.tex|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=4|ti=Operational amplifier circuit|fi=opamp-twopole.tex|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=5|ti=Operational amplifier oscillator|fi=opamp-osc.tex|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=6|ti=Congestion control using RED~\cite{Low+02:infocom}|fi=congctrl-red.tex|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=7|ti=Atomic force microscope with piezo tube|fi=afm-preload.tex|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=8|ti=Drug administration|fi=drugadmin-alcohol.tex|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=9|ti=Population dynamics|fi=logistic.tex|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=10|ti=Fisheries management|fi=fishery-modeling.tex|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=11|ti=|fi=powertrain.tex|st=P|au=|co=|re=}}
 
{{exercise table end}}
 
{{exercise table end}}
  
 
=== {{chlink|Dynamic Behavior}} ===
 
=== {{chlink|Dynamic Behavior}} ===
 
{{exercise table begin}}
 
{{exercise table begin}}
 +
{{exitem|di=|ex=1|ti=Time-invariant systems|fi=timeshift.tex|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=2|ti=Flow in a tank|fi=tank-modeling.tex|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=3|ti=Cruise control|fi=cruise-phaseplot.tex|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=4|ti=Lyapunov functions|fi=lyap-secord.tex|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=5|ti=Damped spring--mass system|fi=lyap-oscillator.tex|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=6|ti=Electric generator|fi=missing|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=7|ti=Lyapunov equation|fi=missing|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=8|ti=Congestion control|fi=congctrl-lyapstab.tex|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=9|ti=Swinging up a pendulum|fi=invpend-swingup.tex|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=10|ti=Root locus diagram|fi=missing|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=11|ti=Discrete-time Lyapunov function|fi=discrete-lyapunov.tex|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=12|ti=Operational amplifier oscillator|fi=opamp-oscnl.tex|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=13|ti=Self-activating genetic circuit|fi=biocircuits-posfbk.tex|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=14|ti=Diagonal systems|fi=missing|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=15|ti=Furuta pendulum|fi=furuta.tex|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=16|ti=Routh-Hurwitz criterion|fi=routh.tex|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=17|ti=|fi=missing|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=18|ti=|fi=missing|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=19|ti=|fi=predprey-limit.tex|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=20|ti=Windup protection by conditional integration|fi=missing|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=21|ti=|fi=missing|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=22|ti=Spike generation in neurons|fi=missing|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=23|ti=|fi=compsys-consensus.tex|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=24|ti=Steering dynamics of a ship|fi=tanker-dynamics.tex|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=25|ti=Pitchfork bifurcation|fi=missing|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=26|ti=|fi=stabexmp-mooregreitzer.tex|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=27|ti=|fi=cruise-lyapunov.tex|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=28|ti=|fi=lyapexmp.tex|st=P|au=|co=|re=}}
 
{{exercise table end}}
 
{{exercise table end}}
  
 
=== {{chlink|Linear Systems}} ===
 
=== {{chlink|Linear Systems}} ===
 
{{exercise table begin}}
 
{{exercise table begin}}
 +
{{exitem|di=|ex=1|ti=Response to the derivative of a signal|fi=missing|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=2|ti=Impulse response and convolution|fi=missing|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=3|ti=Pulse response for a compartment model|fi=compartment-pulse.tex|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=4|ti=Matrix exponential for second-order system|fi=matrixexp.tex|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=5|ti=Lyapunov function for a linear system|fi=missing|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=6|ti=Nondiagonal Jordan form|fi=missing|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=7|ti=Rise time for a first-order system|fi=missing|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=8|ti=Discrete-time systems|fi=discrete-linsys.tex|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=9|ti=Keynesian economics|fi=discrete-keynes.tex|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=10|ti=|fi=missing|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=11|ti=Transcriptional regulation|fi=biocircuits-negfbk.tex|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=12|ti=Normalized coordinates for second-order system|fi=missing|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=13|ti=Matrix exponential for Jordan form|fi=missing|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=14|ti=Solution of a second-order system|fi=missing|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=15|ti=Monotone step response|fi=missing|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=16|ti=|fi=missing|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=17|ti=|fi=missing|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=18|ti=|fi=linexmp-coupled.tex|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=19|ti=State variables in compartment models|fi=compartment-states.tex|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=20|ti=|fi=queue-linsys.tex|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=21|ti=Keynes model in continuous time|fi=missing|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=22|ti=|fi=cartpend.tex|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=23|ti=|fi=missing|st=P|au=|co=|re=}}
 
{{exercise table end}}
 
{{exercise table end}}
  
 
=== {{chlink|State Feedback}} ===
 
=== {{chlink|State Feedback}} ===
 
{{exercise table begin}}
 
{{exercise table begin}}
 +
{{exitem|di=|ex=1|ti=Double integrator|fi=missing|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=2|ti=Reachability from nonzero initial state|fi=missing|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=3|ti=Unreachable systems|fi=missing|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=4|ti=Integral feedback for rejecting constant disturbances|fi=missing|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=5|ti=Rear-steered bicycle|fi=bicycle-rearsteer.tex|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=6|ti=Characteristic polynomial for reachable canonical form|fi=missing|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=7|ti=Reachability matrix for reachable canonical form|fi=missing|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=8|ti=Non-maintainable equilibria|fi=missing|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=9|ti=Eigenvalue assignment for unreachable system|fi=missing|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=10|ti=Cayley--Hamilton theorem|fi=missing|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=11|ti=Motor drive|fi=missing|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=12|ti=Whipple bicycle model|fi=bicycle-whipple.tex|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=13|ti=Atomic force microscope|fi=missing|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=14|ti=|fi=missing|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=15|ti=Bryson's rule|fi=brysons-rule.tex|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=16|ti=|fi=integral-refgain.tex|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=17|ti=Unreachable compartment model|fi=compartment-nonreach.tex|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=18|ti=|fi=missing|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=19|ti=|fi=missing|st=|au=|co=|re=}}
 
{{exercise table end}}
 
{{exercise table end}}
  
 
=== {{chlink|Output Feedback}} ===
 
=== {{chlink|Output Feedback}} ===
 
{{exercise table begin}}
 
{{exercise table begin}}
 +
{{exitem|di=|ex=1|ti=Coordinate transformations|fi=missing|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=2|ti=|fi=missing|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=3|ti=Observable canonical form|fi=missing|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=4|ti=Bicycle dynamics|fi=bicycle-observability.tex|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=5|ti=Integral action|fi=integral-action.tex|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=6|ti=Vectored thrust aircraft|fi=pvtol-ssctrl.tex|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=7|ti=Uniqueness of observers|fi=missing|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=8|ti=Observers using differentiation|fi=diff.tex|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=9|ti=Observer for Teorell's compartment model|fi=compartment-teorellobs.tex|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=10|ti=Observer design for motor drive|fi=dcmotor-observer.tex|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=11|ti=Feedforward design for motor drive|fi=dcmotor-feedforward.tex|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=12|ti=Whipple bicycle model|fi=bicycle-whipple.tex|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=13|ti=Discrete-time random walk|fi=kalman-randomwalk.tex|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=14|ti=Kalman decomposition|fi=missing|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=15|ti=|fi=missing|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=16|ti=Balance system|fi=balance-observable.tex|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=17|ti=Balance system with biased measurement|fi=balance-statectrl.tex|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=18|ti=Duality|fi=missing|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=19|ti=Balance system|fi=missing|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=20|ti=Trajectory generation|fi=trajgen-scalar.tex|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=21|ti=Selection of eigenvalues|fi=missing|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=22|ti=Kalman filter for scalar ODE|fi=kalman-scalar.tex|st=P|au=|co=|re=}}
 
{{exercise table end}}
 
{{exercise table end}}
  
 
=== {{chlink|Transfer Functions}} ===
 
=== {{chlink|Transfer Functions}} ===
 
{{exercise table begin}}
 
{{exercise table begin}}
 +
{{exitem|di=|ex=1|ti=|fi=missing|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=2|ti=|fi=modalinput.tex|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=3|ti=Inverted pendulum|fi=invpend-xferfcn.tex|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=4|ti=Solutions corresponding to poles and zeros|fi=missing|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=5|ti=Operational amplifier|fi=opamp-pictrl.tex|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=6|ti=Transfer function for state space system|fi=missing|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=7|ti=Kalman decomposition|fi=missing|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=8|ti=|fi=missing|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=9|ti=Bode plot for a simple zero|fi=missing|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=10|ti=Vectored thrust aircraft|fi=pvtol-lateraltf.tex|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=11|ti=Common poles|fi=missing|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=12|ti=Congestion control|fi=congctrl-xferfcns.tex|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=13|ti=Inverted pendulum with PD control|fi=invpend-pzcancel.tex|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=14|ti=Vehicle suspension~\cite{hedrick90}|fi=vehicle-quartercar.tex|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=15|ti=Vibration absorber|fi=missing|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=16|ti=|fi=freqexamps.tex|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=17|ti=|fi=model-simplification.tex|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=18|ti=|fi=cruise-pictrl.tex|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=19|ti=|fi=dcmotor-xferfcn.tex|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=20|ti=|fi=missing|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=21|ti=|fi=missing|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=22|ti=|fi=missing|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=23|ti=|fi=missing|st=|au=|co=|re=}}
 
{{exercise table end}}
 
{{exercise table end}}
  
 
=== {{chlink|Frequency Domain Analysis}} ===
 
=== {{chlink|Frequency Domain Analysis}} ===
 
{{exercise table begin}}
 
{{exercise table begin}}
 +
{{exitem|di=|ex=1|ti=Operational amplifier|fi=opamp-unitygain.tex|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=2|ti=Atomic force microscope|fi=afm-tapping.tex|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=3|ti=Heat conduction|fi=missing|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=4|ti=Vectored thrust aircraft|fi=pvtol-looptf.tex|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=5|ti=Vehicle steering|fi=missing|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=6|ti=Stability margins for second-order systems|fi=missing|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=7|ti=Congestion control in overload conditions|fi=congctrl-overload.tex|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=8|ti=Bode's formula|fi=missing|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=9|ti=Pad\'e approximation to a time delay|fi=missing|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=10|ti=Inverse response|fi=missing|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=11|ti=Describing function analysis|fi=missing|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=12|ti=Right half-plane pole|fi=missing|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=13|ti=Third-order system|fi=missing|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=14|ti=|fi=bodenyq.tex|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=15|ti=Congestion control using TCP/Reno|fi=congctrl-margins.tex|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=16|ti=|fi=opamp-routh.tex|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=17|ti=|fi=missing|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=18|ti=Limitations|fi=missing|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=19|ti=Limitations|fi=missing|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=20|ti=Delay differential equations|fi=delayde.tex|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=21|ti=Cruise control design|fi=cruise-pictrl.tex|st=P|au=|co=|re=}}
 
{{exercise table end}}
 
{{exercise table end}}
  
 
=== {{chlink|PID Control}} ===
 
=== {{chlink|PID Control}} ===
 
{{exercise table begin}}
 
{{exercise table begin}}
 +
{{exitem|di=|ex=1|ti=Ideal PID controllers|fi=missing|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=2|ti=|fi=missing|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=3|ti=|fi=missing|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=4|ti=Ziegler--Nichols tuning|fi=missing|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=5|ti=Vehicle steering|fi=steering-pi.tex|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=6|ti=Congestion control|fi=congctrl-pituning.tex|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=7|ti=Motor drive|fi=dcmotor-pdctrl.tex|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=8|ti=|fi=missing|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=9|ti=Tuning rules|fi=missing|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=10|ti=Windup and anti-windup|fi=missing|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=11|ti=Windup protection by conditional integration|fi=missing|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=12|ti=|fi=pidmethods.tex|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=13|ti=|fi=pidexmps.tex|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=14|ti=Compartment model|fi=compartment-monotone.tex|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=15|ti=|fi=missing|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=16|ti=|fi=pirlocus.tex|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=17|ti=|fi=pvtol-pid.tex|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=18|ti=Ball and beam|fi=missing|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=19|ti=|fi=balance-pid.tex|st=P|au=|co=|re=}}
 
{{exercise table end}}
 
{{exercise table end}}
  
 
=== {{chlink|Frequency Domain Synthesis}} ===
 
=== {{chlink|Frequency Domain Synthesis}} ===
 
{{exercise table begin}}
 
{{exercise table begin}}
 +
{{exitem|di=|ex=1|ti=|fi=missing|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=2|ti=|fi=missing|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=3|ti=|fi=missing|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=4|ti=|fi=missing|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=5|ti=Sensitivity of feedback and feedforward|fi=missing|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=6|ti=Equivalence of controllers with two degrees of freedom|fi=missing|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=7|ti=Disturbance attenuation|fi=missing|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=8|ti=Disturbance reduction through feedback|fi=missing|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=9|ti=|fi=missing|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=10|ti=Attenuation of low-frequency sinusoidal disturbances|fi=missing|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=11|ti=|fi=missing|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=12|ti=|fi=missing|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=13|ti=|fi=missing|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=14|ti=Phase margin formulas|fi=missing|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=15|ti=|fi=balance-visual.tex|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=16|ti=Rear-steered bicycle|fi=bicycle-rearsteer.tex|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=17|ti=|fi=missing|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=18|ti=Rise-time/bandwidth product|fi=missing|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=19|ti=|fi=missing|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=20|ti=|fi=znlimits.tex|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=21|ti=Pole in the right half-plane and time delay|fi=missing|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=22|ti=Cancellation of unstable process zero|fi=missing|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=23|ti=Limitations on achievable phase lag|fi=missing|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=24|ti=|fi=missing|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=25|ti=Performance characteristics of second-order systems|fi=secord-perf.tex|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=26|ti=|fi=secord-rhpz.tex|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=27|ti=Integral of complementary sensitivity|fi=missing|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=28|ti=Bode's integral|fi=missing|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=29|ti=Lead compensator for an insect flight control system|fi=flylead.tex|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=30|ti=Control of a magnetic levitation system|fi=maglev.tex|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=31|ti=|fi=missing|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=32|ti=|fi=pvtol-gangof4.tex|st=|au=|co=|re=}}
 
{{exercise table end}}
 
{{exercise table end}}
  
 
=== {{chlink|Robust Performance}} ===
 
=== {{chlink|Robust Performance}} ===
 
{{exercise table begin}}
 
{{exercise table begin}}
 +
{{exitem|di=|ex=1|ti=|fi=missing|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=2|ti=|fi=missing|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=3|ti=Difference in sensitivity functions|fi=missing|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=4|ti=The Riemann sphere|fi=missing|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=5|ti=Stability margins|fi=missing|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=6|ti=Bode's ideal loop transfer function|fi=missing|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=7|ti=|fi=missing|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=8|ti=Smith predictor|fi=missing|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=9|ti=Ideal delay compensator|fi=missing|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=10|ti=Vehicle steering|fi=missing|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=11|ti=|fi=missing|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=12|ti=AFM nanopositioning system|fi=missing|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=13|ti=$H_\infty$ control|fi=missing|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=14|ti=|fi=missing|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=15|ti=|fi=missing|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=16|ti=Robustness using the Nyquist criterion|fi=missing|st=P|au=|co=|re=}}
 +
{{exitem|di=|ex=17|ti=Robustness inequalities|fi=missing|st=|au=|co=|re=}}
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{{exitem|di=|ex=18|ti=|fi=missing|st=|au=|co=|re=}}
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{{exitem|di=|ex=19|ti=|fi=missing|st=|au=|co=|re=}}
 +
{{exitem|di=|ex=20|ti=Disk drive tracking|fi=missing|st=|au=|co=|re=}}
 
{{exercise table end}}
 
{{exercise table end}}

Revision as of 18:56, 1 February 2008

This page contains a list of the exercises in the text, including supplemental problems. It is mainly intended for use by people who are generating solutions to the exercises.

Guide to entries

Each entry in the table below contains the following information (the two-letter code in parenthesis is used in the table entry macros):

  • Exercise number (ex): the number of the exercise in the solutions manual. Items marked with a * appear in the printed version of the text.
  • Directory (di): the name of the subdirectory where the exercise appears. This does not appear in the table directly, but is used to create the link to the exercise.
  • Title (ti): a short descriptive title for the exercise.
  • Filename (fi): the base filename used for the exercise. Clicking on the link will take you to the LaTeX source code for the exercise (requires login).
  • Solution status (st): current status of the solutions. The following abbreviations are used:
    • C (complete) - complete solution is available
    • P (partial) - partial or preliminary solution is available
    • I (in progress) - solution is being written, but is not yet available
    • U (unavailable) - no solution is currently available
    • X (not planned) - no solution is planned
  • Author (au): initials for the author of the solutions
  • Comment (co): additional comments.

How to sign up to write a solution for an exercise:

  1. Find an exercise whose solution status is either unavailable (U) or partial (P)
  2. Edit the table and add your name to the 're' entry in the table
  3. Add the page to your watch list so that you can see when there is a change in status
  4. Wait until you are assigned a set of problems to work on (status will be changed to 'I', with your initials listed in the author column.

Chapter 1 - Introduction

Num Title Filename Stat Auth Comments
1.1* Occular motion eyemotion C KJA
1.2* Feedback examples fbkexamps C Misc
1.3* Human balance balance-human U Open
1.4* Cruise control redesign cruise-redesign U Open
1.5* Integral action integral C KJA
1.6* Popular press articles nytexamps C
1.7 Milk supply chain milksupply P KJA Figure missing
1.8 MATLAB cruise control cruise-mlintro P Misc Preliminary solution available; could be cleaned up
1.9 MATLAB ball and beam ballbeam-mlintro P Misc Preliminary solution available; could be cleaned up
1.10 Web search: voltage clamp voltageclamp U Give short intro plus web links
1.11 Web search: haptics and force feedback haptics U Give short intro plus web links
1.12 Anti-rollover control rollover U Give short summary of regulations

Chapter 2 - System Modeling

Num Title Filename Stat Auth Comments
1 Chain of integrators form chainofint.tex
2 Inverted pendulum balance-bal2inv.tex P
3 Disrete-time dynamics discrete-solutions.tex P
4 Keynesian economics discrete-keynes.tex
5 Least squares system identification sysid-leastsq.tex
6 Normalized oscillator dynamics oscillator.tex P
7 Electric generator powergrid.tex P
8 Admission control for a queue queue-admcontrol.tex P
9 Biological switch biocircuits-switchmod.tex P
10 Motor drive dcmotor-modeling.tex P
11 Uncertainty lemon lemon.tex P
12 Frequency response freqresp.tex
13 Eye and head motion occular-blockdiag.tex P
14 Second-order system identification sysid-logdec.tex
15 Insect vision flyvision.tex P
16 State space model for balance systems balance-statespace.tex
17 fingerflame.tex P
18 Consensus and invariants compsys-invariants.tex P
19 Electric motor electricmotor.tex P
20 exothermic.tex
21 caffeine.tex P
22 ballbeam-modeling.tex P
23 pvtol2invpend.tex
24 flyflight.tex
25 pendulum.tex P

Chapter 3 - Examples

Num Title Filename Stat Auth Comments
1 Cruise control cruise-hillsim.tex
2 Bicycle dynamics bicycle-statespace.tex
3 Bicycle steering bicycle-steering.tex
4 Operational amplifier circuit opamp-twopole.tex P
5 Operational amplifier oscillator opamp-osc.tex P
6 Congestion control using RED~\cite{Low+02:infocom} congctrl-red.tex P
7 Atomic force microscope with piezo tube afm-preload.tex P
8 Drug administration drugadmin-alcohol.tex
9 Population dynamics logistic.tex
10 Fisheries management fishery-modeling.tex P
11 powertrain.tex P

Chapter 4 - Dynamic Behavior

Num Title Filename Stat Auth Comments
1 Time-invariant systems timeshift.tex
2 Flow in a tank tank-modeling.tex P
3 Cruise control cruise-phaseplot.tex P
4 Lyapunov functions lyap-secord.tex P
5 Damped spring--mass system lyap-oscillator.tex P
6 Electric generator missing P
7 Lyapunov equation missing
8 Congestion control congctrl-lyapstab.tex P
9 Swinging up a pendulum invpend-swingup.tex P
10 Root locus diagram missing P
11 Discrete-time Lyapunov function discrete-lyapunov.tex
12 Operational amplifier oscillator opamp-oscnl.tex P
13 Self-activating genetic circuit biocircuits-posfbk.tex P
14 Diagonal systems missing P
15 Furuta pendulum furuta.tex P
16 Routh-Hurwitz criterion routh.tex
17 missing
18 missing P
19 predprey-limit.tex P
20 Windup protection by conditional integration missing P
21 missing
22 Spike generation in neurons missing P
23 compsys-consensus.tex
24 Steering dynamics of a ship tanker-dynamics.tex P
25 Pitchfork bifurcation missing
26 stabexmp-mooregreitzer.tex P
27 cruise-lyapunov.tex P
28 lyapexmp.tex P

Chapter 5 - Linear Systems

Num Title Filename Stat Auth Comments
1 Response to the derivative of a signal missing
2 Impulse response and convolution missing
3 Pulse response for a compartment model compartment-pulse.tex
4 Matrix exponential for second-order system matrixexp.tex P
5 Lyapunov function for a linear system missing
6 Nondiagonal Jordan form missing P
7 Rise time for a first-order system missing
8 Discrete-time systems discrete-linsys.tex P
9 Keynesian economics discrete-keynes.tex
10 missing P
11 Transcriptional regulation biocircuits-negfbk.tex P
12 Normalized coordinates for second-order system missing
13 Matrix exponential for Jordan form missing
14 Solution of a second-order system missing
15 Monotone step response missing
16 missing P
17 missing P
18 linexmp-coupled.tex P
19 State variables in compartment models compartment-states.tex
20 queue-linsys.tex P
21 Keynes model in continuous time missing
22 cartpend.tex P
23 missing P

Chapter 6 - State Feedback

Num Title Filename Stat Auth Comments
1 Double integrator missing P
2 Reachability from nonzero initial state missing
3 Unreachable systems missing
4 Integral feedback for rejecting constant disturbances missing
5 Rear-steered bicycle bicycle-rearsteer.tex P
6 Characteristic polynomial for reachable canonical form missing
7 Reachability matrix for reachable canonical form missing P
8 Non-maintainable equilibria missing P
9 Eigenvalue assignment for unreachable system missing P
10 Cayley--Hamilton theorem missing
11 Motor drive missing
12 Whipple bicycle model bicycle-whipple.tex P
13 Atomic force microscope missing
14 missing P
15 Bryson's rule brysons-rule.tex
16 integral-refgain.tex
17 Unreachable compartment model compartment-nonreach.tex P
18 missing
19 missing

Chapter 7 - Output Feedback

Num Title Filename Stat Auth Comments
1 Coordinate transformations missing
2 missing
3 Observable canonical form missing
4 Bicycle dynamics bicycle-observability.tex P
5 Integral action integral-action.tex P
6 Vectored thrust aircraft pvtol-ssctrl.tex P
7 Uniqueness of observers missing
8 Observers using differentiation diff.tex
9 Observer for Teorell's compartment model compartment-teorellobs.tex P
10 Observer design for motor drive dcmotor-observer.tex P
11 Feedforward design for motor drive dcmotor-feedforward.tex P
12 Whipple bicycle model bicycle-whipple.tex
13 Discrete-time random walk kalman-randomwalk.tex P
14 Kalman decomposition missing
15 missing
16 Balance system balance-observable.tex
17 Balance system with biased measurement balance-statectrl.tex
18 Duality missing
19 Balance system missing
20 Trajectory generation trajgen-scalar.tex
21 Selection of eigenvalues missing
22 Kalman filter for scalar ODE kalman-scalar.tex P

Chapter 8 - Transfer Functions

Num Title Filename Stat Auth Comments
1 missing
2 modalinput.tex P
3 Inverted pendulum invpend-xferfcn.tex P
4 Solutions corresponding to poles and zeros missing P
5 Operational amplifier opamp-pictrl.tex P
6 Transfer function for state space system missing P
7 Kalman decomposition missing
8 missing
9 Bode plot for a simple zero missing
10 Vectored thrust aircraft pvtol-lateraltf.tex P
11 Common poles missing
12 Congestion control congctrl-xferfcns.tex P
13 Inverted pendulum with PD control invpend-pzcancel.tex P
14 Vehicle suspension~\cite{hedrick90} vehicle-quartercar.tex
15 Vibration absorber missing P
16 freqexamps.tex P
17 model-simplification.tex
18 cruise-pictrl.tex P
19 dcmotor-xferfcn.tex
20 missing
21 missing P
22 missing
23 missing

Chapter 9 - Frequency Domain Analysis

Num Title Filename Stat Auth Comments
1 Operational amplifier opamp-unitygain.tex P
2 Atomic force microscope afm-tapping.tex
3 Heat conduction missing P
4 Vectored thrust aircraft pvtol-looptf.tex P
5 Vehicle steering missing
6 Stability margins for second-order systems missing P
7 Congestion control in overload conditions congctrl-overload.tex P
8 Bode's formula missing
9 Pad\'e approximation to a time delay missing
10 Inverse response missing P
11 Describing function analysis missing
12 Right half-plane pole missing P
13 Third-order system missing
14 bodenyq.tex P
15 Congestion control using TCP/Reno congctrl-margins.tex
16 opamp-routh.tex P
17 missing P
18 Limitations missing
19 Limitations missing
20 Delay differential equations delayde.tex P
21 Cruise control design cruise-pictrl.tex P

Chapter 10 - PID Control

Num Title Filename Stat Auth Comments
1 Ideal PID controllers missing
2 missing
3 missing P
4 Ziegler--Nichols tuning missing P
5 Vehicle steering steering-pi.tex P
6 Congestion control congctrl-pituning.tex P
7 Motor drive dcmotor-pdctrl.tex P
8 missing
9 Tuning rules missing P
10 Windup and anti-windup missing
11 Windup protection by conditional integration missing P
12 pidmethods.tex P
13 pidexmps.tex P
14 Compartment model compartment-monotone.tex
15 missing P
16 pirlocus.tex P
17 pvtol-pid.tex P
18 Ball and beam missing
19 balance-pid.tex P

Chapter 11 - Frequency Domain Synthesis

Num Title Filename Stat Auth Comments
1 missing
2 missing
3 missing P
4 missing
5 Sensitivity of feedback and feedforward missing
6 Equivalence of controllers with two degrees of freedom missing
7 Disturbance attenuation missing
8 Disturbance reduction through feedback missing P
9 missing
10 Attenuation of low-frequency sinusoidal disturbances missing P
11 missing
12 missing P
13 missing P
14 Phase margin formulas missing
15 balance-visual.tex P
16 Rear-steered bicycle bicycle-rearsteer.tex P
17 missing P
18 Rise-time/bandwidth product missing
19 missing P
20 znlimits.tex
21 Pole in the right half-plane and time delay missing P
22 Cancellation of unstable process zero missing
23 Limitations on achievable phase lag missing P
24 missing
25 Performance characteristics of second-order systems secord-perf.tex P
26 secord-rhpz.tex P
27 Integral of complementary sensitivity missing P
28 Bode's integral missing P
29 Lead compensator for an insect flight control system flylead.tex P
30 Control of a magnetic levitation system maglev.tex P
31 missing P
32 pvtol-gangof4.tex

Chapter 12 - Robust Performance

Num Title Filename Stat Auth Comments
1 missing P
2 missing P
3 Difference in sensitivity functions missing P
4 The Riemann sphere missing P
5 Stability margins missing
6 Bode's ideal loop transfer function missing P
7 missing P
8 Smith predictor missing
9 Ideal delay compensator missing
10 Vehicle steering missing
11 missing
12 AFM nanopositioning system missing
13 $H_\infty$ control missing
14 missing
15 missing P
16 Robustness using the Nyquist criterion missing P
17 Robustness inequalities missing
18 missing
19 missing
20 Disk drive tracking missing