Difference between revisions of "Solutions"

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=== {{chlink|Examples}} ===
 
=== {{chlink|Examples}} ===
 
{{exercise table begin}}
 
{{exercise table begin}}
{{exitem|di=examples|ex=1|ti=Cruise control|fi=cruise-hillsim.tex|st=|au=|co=|re=}}
+
{{exitem|di=examples|ex=3.1|ti=Cruise control|fi=cruise-hillsim.tex|st=|au=|co=|re=}}
{{exitem|di=examples|ex=2|ti=Bicycle dynamics|fi=bicycle-statespace.tex|st=|au=|co=|re=}}
+
{{exitem|di=examples|ex=3.2|ti=Bicycle dynamics|fi=bicycle-statespace.tex|st=|au=|co=|re=}}
{{exitem|di=examples|ex=3|ti=Bicycle steering|fi=bicycle-steering.tex|st=|au=|co=|re=}}
+
{{exitem|di=examples|ex=3.3|ti=Bicycle steering|fi=bicycle-steering.tex|st=|au=|co=|re=}}
{{exitem|di=examples|ex=4|ti=Operational amplifier circuit|fi=opamp-twopole.tex|st=P|au=|co=|re=}}
+
{{exitem|di=examples|ex=3.4|ti=Operational amplifier circuit|fi=opamp-twopole.tex|st=P|au=|co=|re=}}
{{exitem|di=examples|ex=5|ti=Operational amplifier oscillator|fi=opamp-osc.tex|st=P|au=|co=|re=}}
+
{{exitem|di=examples|ex=3.5|ti=Operational amplifier oscillator|fi=opamp-osc.tex|st=P|au=|co=|re=}}
{{exitem|di=examples|ex=6|ti=Congestion control using RED~\cite{Low+02:infocom}|fi=congctrl-red.tex|st=P|au=|co=|re=}}
+
{{exitem|di=examples|ex=3.6|ti=Congestion control using RED~\cite{Low+02:infocom}|fi=congctrl-red.tex|st=P|au=|co=|re=}}
{{exitem|di=examples|ex=7|ti=Atomic force microscope with piezo tube|fi=afm-preload.tex|st=P|au=|co=|re=}}
+
{{exitem|di=examples|ex=3.7|ti=Atomic force microscope with piezo tube|fi=afm-preload.tex|st=P|au=|co=|re=}}
{{exitem|di=examples|ex=8|ti=Drug administration|fi=drugadmin-alcohol.tex|st=|au=|co=|re=}}
+
{{exitem|di=examples|ex=3.8|ti=Drug administration|fi=drugadmin-alcohol.tex|st=|au=|co=|re=}}
{{exitem|di=examples|ex=9|ti=Population dynamics|fi=logistic.tex|st=|au=|co=|re=}}
+
{{exitem|di=examples|ex=3.9|ti=Population dynamics|fi=logistic.tex|st=|au=|co=|re=}}
{{exitem|di=examples|ex=10|ti=Fisheries management|fi=fishery-modeling.tex|st=P|au=|co=|re=}}
+
{{exitem|di=examples|ex=3.10|ti=Fisheries management|fi=fishery-modeling.tex|st=P|au=|co=|re=}}
{{exitem|di=examples|ex=11|ti=|fi=powertrain.tex|st=P|au=|co=|re=}}
+
{{exitem|di=examples|ex=3.11|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=dynamics|ex=1|ti=Time-invariant systems|fi=timeshift.tex|st=|au=|co=|re=}}
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{{exitem|di=dynamics|ex=4.1|ti=Time-invariant systems|fi=timeshift.tex|st=|au=|co=|re=}}
{{exitem|di=dynamics|ex=2|ti=Flow in a tank|fi=tank-modeling.tex|st=P|au=|co=|re=}}
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{{exitem|di=dynamics|ex=4.2|ti=Flow in a tank|fi=tank-modeling.tex|st=P|au=|co=|re=}}
{{exitem|di=dynamics|ex=3|ti=Cruise control|fi=cruise-phaseplot.tex|st=P|au=|co=|re=}}
+
{{exitem|di=dynamics|ex=4.3|ti=Cruise control|fi=cruise-phaseplot.tex|st=P|au=|co=|re=}}
{{exitem|di=dynamics|ex=4|ti=Lyapunov functions|fi=lyap-secord.tex|st=P|au=|co=|re=}}
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{{exitem|di=dynamics|ex=4.4|ti=Lyapunov functions|fi=lyap-secord.tex|st=P|au=|co=|re=}}
{{exitem|di=dynamics|ex=5|ti=Damped spring--mass system|fi=lyap-oscillator.tex|st=P|au=|co=|re=}}
+
{{exitem|di=dynamics|ex=4.5|ti=Damped spring--mass system|fi=lyap-oscillator.tex|st=P|au=|co=|re=}}
{{exitem|di=dynamics|ex=6|ti=Electric generator|fi=missing|st=P|au=|co=|re=}}
+
{{exitem|di=dynamics|ex=4.6|ti=Electric generator|fi=missing|st=P|au=|co=|re=}}
{{exitem|di=dynamics|ex=7|ti=Lyapunov equation|fi=missing|st=|au=|co=|re=}}
+
{{exitem|di=dynamics|ex=4.7|ti=Lyapunov equation|fi=missing|st=|au=|co=|re=}}
{{exitem|di=dynamics|ex=8|ti=Congestion control|fi=congctrl-lyapstab.tex|st=P|au=|co=|re=}}
+
{{exitem|di=dynamics|ex=4.8|ti=Congestion control|fi=congctrl-lyapstab.tex|st=P|au=|co=|re=}}
{{exitem|di=dynamics|ex=9|ti=Swinging up a pendulum|fi=invpend-swingup.tex|st=P|au=|co=|re=}}
+
{{exitem|di=dynamics|ex=4.9|ti=Swinging up a pendulum|fi=invpend-swingup.tex|st=P|au=|co=|re=}}
{{exitem|di=dynamics|ex=10|ti=Root locus diagram|fi=missing|st=P|au=|co=|re=}}
+
{{exitem|di=dynamics|ex=4.10|ti=Root locus diagram|fi=missing|st=P|au=|co=|re=}}
{{exitem|di=dynamics|ex=11|ti=Discrete-time Lyapunov function|fi=discrete-lyapunov.tex|st=|au=|co=|re=}}
+
{{exitem|di=dynamics|ex=4.11|ti=Discrete-time Lyapunov function|fi=discrete-lyapunov.tex|st=|au=|co=|re=}}
{{exitem|di=dynamics|ex=12|ti=Operational amplifier oscillator|fi=opamp-oscnl.tex|st=P|au=|co=|re=}}
+
{{exitem|di=dynamics|ex=4.12|ti=Operational amplifier oscillator|fi=opamp-oscnl.tex|st=P|au=|co=|re=}}
{{exitem|di=dynamics|ex=13|ti=Self-activating genetic circuit|fi=biocircuits-posfbk.tex|st=P|au=|co=|re=}}
+
{{exitem|di=dynamics|ex=4.13|ti=Self-activating genetic circuit|fi=biocircuits-posfbk.tex|st=P|au=|co=|re=}}
{{exitem|di=dynamics|ex=14|ti=Diagonal systems|fi=missing|st=P|au=|co=|re=}}
+
{{exitem|di=dynamics|ex=4.14|ti=Diagonal systems|fi=missing|st=P|au=|co=|re=}}
{{exitem|di=dynamics|ex=15|ti=Furuta pendulum|fi=furuta.tex|st=P|au=|co=|re=}}
+
{{exitem|di=dynamics|ex=4.15|ti=Furuta pendulum|fi=furuta.tex|st=P|au=|co=|re=}}
{{exitem|di=dynamics|ex=16|ti=Routh-Hurwitz criterion|fi=routh.tex|st=|au=|co=|re=}}
+
{{exitem|di=dynamics|ex=4.16|ti=Routh-Hurwitz criterion|fi=routh.tex|st=|au=|co=|re=}}
{{exitem|di=dynamics|ex=17|ti=|fi=missing|st=|au=|co=|re=}}
+
{{exitem|di=dynamics|ex=4.17|ti=|fi=missing|st=|au=|co=|re=}}
{{exitem|di=dynamics|ex=18|ti=|fi=missing|st=P|au=|co=|re=}}
+
{{exitem|di=dynamics|ex=4.18|ti=|fi=missing|st=P|au=|co=|re=}}
{{exitem|di=dynamics|ex=19|ti=|fi=predprey-limit.tex|st=P|au=|co=|re=}}
+
{{exitem|di=dynamics|ex=4.19|ti=|fi=predprey-limit.tex|st=P|au=|co=|re=}}
{{exitem|di=dynamics|ex=20|ti=Windup protection by conditional integration|fi=missing|st=P|au=|co=|re=}}
+
{{exitem|di=dynamics|ex=4.20|ti=Windup protection by conditional integration|fi=missing|st=P|au=|co=|re=}}
{{exitem|di=dynamics|ex=21|ti=|fi=missing|st=|au=|co=|re=}}
+
{{exitem|di=dynamics|ex=4.21|ti=|fi=missing|st=|au=|co=|re=}}
{{exitem|di=dynamics|ex=22|ti=Spike generation in neurons|fi=missing|st=P|au=|co=|re=}}
+
{{exitem|di=dynamics|ex=4.22|ti=Spike generation in neurons|fi=missing|st=P|au=|co=|re=}}
{{exitem|di=dynamics|ex=23|ti=|fi=compsys-consensus.tex|st=|au=|co=|re=}}
+
{{exitem|di=dynamics|ex=4.23|ti=|fi=compsys-consensus.tex|st=|au=|co=|re=}}
{{exitem|di=dynamics|ex=24|ti=Steering dynamics of a ship|fi=tanker-dynamics.tex|st=P|au=|co=|re=}}
+
{{exitem|di=dynamics|ex=4.24|ti=Steering dynamics of a ship|fi=tanker-dynamics.tex|st=P|au=|co=|re=}}
{{exitem|di=dynamics|ex=25|ti=Pitchfork bifurcation|fi=missing|st=|au=|co=|re=}}
+
{{exitem|di=dynamics|ex=4.25|ti=Pitchfork bifurcation|fi=missing|st=|au=|co=|re=}}
{{exitem|di=dynamics|ex=26|ti=|fi=stabexmp-mooregreitzer.tex|st=P|au=|co=|re=}}
+
{{exitem|di=dynamics|ex=4.26|ti=|fi=stabexmp-mooregreitzer.tex|st=P|au=|co=|re=}}
{{exitem|di=dynamics|ex=27|ti=|fi=cruise-lyapunov.tex|st=P|au=|co=|re=}}
+
{{exitem|di=dynamics|ex=4.27|ti=|fi=cruise-lyapunov.tex|st=P|au=|co=|re=}}
{{exitem|di=dynamics|ex=28|ti=|fi=lyapexmp.tex|st=P|au=|co=|re=}}
+
{{exitem|di=dynamics|ex=4.28|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=linsys|ex=1|ti=Response to the derivative of a signal|fi=missing|st=|au=|co=|re=}}
+
{{exitem|di=linsys|ex=5.1|ti=Response to the derivative of a signal|fi=missing|st=|au=|co=|re=}}
{{exitem|di=linsys|ex=2|ti=Impulse response and convolution|fi=missing|st=|au=|co=|re=}}
+
{{exitem|di=linsys|ex=5.2|ti=Impulse response and convolution|fi=missing|st=|au=|co=|re=}}
{{exitem|di=linsys|ex=3|ti=Pulse response for a compartment model|fi=compartment-pulse.tex|st=|au=|co=|re=}}
+
{{exitem|di=linsys|ex=5.3|ti=Pulse response for a compartment model|fi=compartment-pulse.tex|st=|au=|co=|re=}}
{{exitem|di=linsys|ex=4|ti=Matrix exponential for second-order system|fi=matrixexp.tex|st=P|au=|co=|re=}}
+
{{exitem|di=linsys|ex=5.4|ti=Matrix exponential for second-order system|fi=matrixexp.tex|st=P|au=|co=|re=}}
{{exitem|di=linsys|ex=5|ti=Lyapunov function for a linear system|fi=missing|st=|au=|co=|re=}}
+
{{exitem|di=linsys|ex=5.5|ti=Lyapunov function for a linear system|fi=missing|st=|au=|co=|re=}}
{{exitem|di=linsys|ex=6|ti=Nondiagonal Jordan form|fi=missing|st=P|au=|co=|re=}}
+
{{exitem|di=linsys|ex=5.6|ti=Nondiagonal Jordan form|fi=missing|st=P|au=|co=|re=}}
{{exitem|di=linsys|ex=7|ti=Rise time for a first-order system|fi=missing|st=|au=|co=|re=}}
+
{{exitem|di=linsys|ex=5.7|ti=Rise time for a first-order system|fi=missing|st=|au=|co=|re=}}
{{exitem|di=linsys|ex=8|ti=Discrete-time systems|fi=discrete-linsys.tex|st=P|au=|co=|re=}}
+
{{exitem|di=linsys|ex=5.8|ti=Discrete-time systems|fi=discrete-linsys.tex|st=P|au=|co=|re=}}
{{exitem|di=linsys|ex=9|ti=Keynesian economics|fi=discrete-keynes.tex|st=|au=|co=|re=}}
+
{{exitem|di=linsys|ex=5.9|ti=Keynesian economics|fi=discrete-keynes.tex|st=|au=|co=|re=}}
{{exitem|di=linsys|ex=10|ti=|fi=missing|st=P|au=|co=|re=}}
+
{{exitem|di=linsys|ex=5.10|ti=|fi=missing|st=P|au=|co=|re=}}
{{exitem|di=linsys|ex=11|ti=Transcriptional regulation|fi=biocircuits-negfbk.tex|st=P|au=|co=|re=}}
+
{{exitem|di=linsys|ex=5.11|ti=Transcriptional regulation|fi=biocircuits-negfbk.tex|st=P|au=|co=|re=}}
{{exitem|di=linsys|ex=12|ti=Normalized coordinates for second-order system|fi=missing|st=|au=|co=|re=}}
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{{exitem|di=linsys|ex=5.12|ti=Normalized coordinates for second-order system|fi=missing|st=|au=|co=|re=}}
{{exitem|di=linsys|ex=13|ti=Matrix exponential for Jordan form|fi=missing|st=|au=|co=|re=}}
+
{{exitem|di=linsys|ex=5.13|ti=Matrix exponential for Jordan form|fi=missing|st=|au=|co=|re=}}
{{exitem|di=linsys|ex=14|ti=Solution of a second-order system|fi=missing|st=|au=|co=|re=}}
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{{exitem|di=linsys|ex=5.14|ti=Solution of a second-order system|fi=missing|st=|au=|co=|re=}}
{{exitem|di=linsys|ex=15|ti=Monotone step response|fi=missing|st=|au=|co=|re=}}
+
{{exitem|di=linsys|ex=5.15|ti=Monotone step response|fi=missing|st=|au=|co=|re=}}
{{exitem|di=linsys|ex=16|ti=|fi=missing|st=P|au=|co=|re=}}
+
{{exitem|di=linsys|ex=5.16|ti=|fi=missing|st=P|au=|co=|re=}}
{{exitem|di=linsys|ex=17|ti=|fi=missing|st=P|au=|co=|re=}}
+
{{exitem|di=linsys|ex=5.17|ti=|fi=missing|st=P|au=|co=|re=}}
{{exitem|di=linsys|ex=18|ti=|fi=linexmp-coupled.tex|st=P|au=|co=|re=}}
+
{{exitem|di=linsys|ex=5.18|ti=|fi=linexmp-coupled.tex|st=P|au=|co=|re=}}
{{exitem|di=linsys|ex=19|ti=State variables in compartment models|fi=compartment-states.tex|st=|au=|co=|re=}}
+
{{exitem|di=linsys|ex=5.19|ti=State variables in compartment models|fi=compartment-states.tex|st=|au=|co=|re=}}
{{exitem|di=linsys|ex=20|ti=|fi=queue-linsys.tex|st=P|au=|co=|re=}}
+
{{exitem|di=linsys|ex=5.20|ti=|fi=queue-linsys.tex|st=P|au=|co=|re=}}
{{exitem|di=linsys|ex=21|ti=Keynes model in continuous time|fi=missing|st=|au=|co=|re=}}
+
{{exitem|di=linsys|ex=5.21|ti=Keynes model in continuous time|fi=missing|st=|au=|co=|re=}}
{{exitem|di=linsys|ex=22|ti=|fi=cartpend.tex|st=P|au=|co=|re=}}
+
{{exitem|di=linsys|ex=5.22|ti=|fi=cartpend.tex|st=P|au=|co=|re=}}
{{exitem|di=linsys|ex=23|ti=|fi=missing|st=P|au=|co=|re=}}
+
{{exitem|di=linsys|ex=5.23|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=statefbk|ex=1|ti=Double integrator|fi=missing|st=P|au=|co=|re=}}
+
{{exitem|di=statefbk|ex=6.1|ti=Double integrator|fi=missing|st=P|au=|co=|re=}}
{{exitem|di=statefbk|ex=2|ti=Reachability from nonzero initial state|fi=missing|st=|au=|co=|re=}}
+
{{exitem|di=statefbk|ex=6.2|ti=Reachability from nonzero initial state|fi=missing|st=|au=|co=|re=}}
{{exitem|di=statefbk|ex=3|ti=Unreachable systems|fi=missing|st=|au=|co=|re=}}
+
{{exitem|di=statefbk|ex=6.3|ti=Unreachable systems|fi=missing|st=|au=|co=|re=}}
{{exitem|di=statefbk|ex=4|ti=Integral feedback for rejecting constant disturbances|fi=missing|st=|au=|co=|re=}}
+
{{exitem|di=statefbk|ex=6.4|ti=Integral feedback for rejecting constant disturbances|fi=missing|st=|au=|co=|re=}}
{{exitem|di=statefbk|ex=5|ti=Rear-steered bicycle|fi=bicycle-rearsteer.tex|st=P|au=|co=|re=}}
+
{{exitem|di=statefbk|ex=6.5|ti=Rear-steered bicycle|fi=bicycle-rearsteer.tex|st=P|au=|co=|re=}}
{{exitem|di=statefbk|ex=6|ti=Characteristic polynomial for reachable canonical form|fi=missing|st=|au=|co=|re=}}
+
{{exitem|di=statefbk|ex=6.6|ti=Characteristic polynomial for reachable canonical form|fi=missing|st=|au=|co=|re=}}
{{exitem|di=statefbk|ex=7|ti=Reachability matrix for reachable canonical form|fi=missing|st=P|au=|co=|re=}}
+
{{exitem|di=statefbk|ex=6.7|ti=Reachability matrix for reachable canonical form|fi=missing|st=P|au=|co=|re=}}
{{exitem|di=statefbk|ex=8|ti=Non-maintainable equilibria|fi=missing|st=P|au=|co=|re=}}
+
{{exitem|di=statefbk|ex=6.8|ti=Non-maintainable equilibria|fi=missing|st=P|au=|co=|re=}}
{{exitem|di=statefbk|ex=9|ti=Eigenvalue assignment for unreachable system|fi=missing|st=P|au=|co=|re=}}
+
{{exitem|di=statefbk|ex=6.9|ti=Eigenvalue assignment for unreachable system|fi=missing|st=P|au=|co=|re=}}
{{exitem|di=statefbk|ex=10|ti=Cayley--Hamilton theorem|fi=missing|st=|au=|co=|re=}}
+
{{exitem|di=statefbk|ex=6.10|ti=Cayley--Hamilton theorem|fi=missing|st=|au=|co=|re=}}
{{exitem|di=statefbk|ex=11|ti=Motor drive|fi=missing|st=|au=|co=|re=}}
+
{{exitem|di=statefbk|ex=6.11|ti=Motor drive|fi=missing|st=|au=|co=|re=}}
{{exitem|di=statefbk|ex=12|ti=Whipple bicycle model|fi=bicycle-whipple.tex|st=P|au=|co=|re=}}
+
{{exitem|di=statefbk|ex=6.12|ti=Whipple bicycle model|fi=bicycle-whipple.tex|st=P|au=|co=|re=}}
{{exitem|di=statefbk|ex=13|ti=Atomic force microscope|fi=missing|st=|au=|co=|re=}}
+
{{exitem|di=statefbk|ex=6.13|ti=Atomic force microscope|fi=missing|st=|au=|co=|re=}}
{{exitem|di=statefbk|ex=14|ti=|fi=missing|st=P|au=|co=|re=}}
+
{{exitem|di=statefbk|ex=6.14|ti=|fi=missing|st=P|au=|co=|re=}}
{{exitem|di=statefbk|ex=15|ti=Bryson's rule|fi=brysons-rule.tex|st=|au=|co=|re=}}
+
{{exitem|di=statefbk|ex=6.15|ti=Bryson's rule|fi=brysons-rule.tex|st=|au=|co=|re=}}
{{exitem|di=statefbk|ex=16|ti=|fi=integral-refgain.tex|st=|au=|co=|re=}}
+
{{exitem|di=statefbk|ex=6.16|ti=|fi=integral-refgain.tex|st=|au=|co=|re=}}
{{exitem|di=statefbk|ex=17|ti=Unreachable compartment model|fi=compartment-nonreach.tex|st=P|au=|co=|re=}}
+
{{exitem|di=statefbk|ex=6.17|ti=Unreachable compartment model|fi=compartment-nonreach.tex|st=P|au=|co=|re=}}
{{exitem|di=statefbk|ex=18|ti=|fi=missing|st=|au=|co=|re=}}
+
{{exitem|di=statefbk|ex=6.18|ti=|fi=missing|st=|au=|co=|re=}}
{{exitem|di=statefbk|ex=19|ti=|fi=missing|st=|au=|co=|re=}}
+
{{exitem|di=statefbk|ex=6.19|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=outputfbk|ex=1|ti=Coordinate transformations|fi=missing|st=|au=|co=|re=}}
+
{{exitem|di=outputfbk|ex=7.1|ti=Coordinate transformations|fi=missing|st=|au=|co=|re=}}
{{exitem|di=outputfbk|ex=2|ti=|fi=missing|st=|au=|co=|re=}}
+
{{exitem|di=outputfbk|ex=7.2|ti=|fi=missing|st=|au=|co=|re=}}
{{exitem|di=outputfbk|ex=3|ti=Observable canonical form|fi=missing|st=|au=|co=|re=}}
+
{{exitem|di=outputfbk|ex=7.3|ti=Observable canonical form|fi=missing|st=|au=|co=|re=}}
{{exitem|di=outputfbk|ex=4|ti=Bicycle dynamics|fi=bicycle-observability.tex|st=P|au=|co=|re=}}
+
{{exitem|di=outputfbk|ex=7.4|ti=Bicycle dynamics|fi=bicycle-observability.tex|st=P|au=|co=|re=}}
{{exitem|di=outputfbk|ex=5|ti=Integral action|fi=integral-action.tex|st=P|au=|co=|re=}}
+
{{exitem|di=outputfbk|ex=7.5|ti=Integral action|fi=integral-action.tex|st=P|au=|co=|re=}}
{{exitem|di=outputfbk|ex=6|ti=Vectored thrust aircraft|fi=pvtol-ssctrl.tex|st=P|au=|co=|re=}}
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{{exitem|di=outputfbk|ex=7.6|ti=Vectored thrust aircraft|fi=pvtol-ssctrl.tex|st=P|au=|co=|re=}}
{{exitem|di=outputfbk|ex=7|ti=Uniqueness of observers|fi=missing|st=|au=|co=|re=}}
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{{exitem|di=outputfbk|ex=7.7|ti=Uniqueness of observers|fi=missing|st=|au=|co=|re=}}
{{exitem|di=outputfbk|ex=8|ti=Observers using differentiation|fi=diff.tex|st=|au=|co=|re=}}
+
{{exitem|di=outputfbk|ex=7.8|ti=Observers using differentiation|fi=diff.tex|st=|au=|co=|re=}}
{{exitem|di=outputfbk|ex=9|ti=Observer for Teorell's compartment model|fi=compartment-teorellobs.tex|st=P|au=|co=|re=}}
+
{{exitem|di=outputfbk|ex=7.9|ti=Observer for Teorell's compartment model|fi=compartment-teorellobs.tex|st=P|au=|co=|re=}}
{{exitem|di=outputfbk|ex=10|ti=Observer design for motor drive|fi=dcmotor-observer.tex|st=P|au=|co=|re=}}
+
{{exitem|di=outputfbk|ex=7.10|ti=Observer design for motor drive|fi=dcmotor-observer.tex|st=P|au=|co=|re=}}
{{exitem|di=outputfbk|ex=11|ti=Feedforward design for motor drive|fi=dcmotor-feedforward.tex|st=P|au=|co=|re=}}
+
{{exitem|di=outputfbk|ex=7.11|ti=Feedforward design for motor drive|fi=dcmotor-feedforward.tex|st=P|au=|co=|re=}}
{{exitem|di=outputfbk|ex=12|ti=Whipple bicycle model|fi=bicycle-whipple.tex|st=|au=|co=|re=}}
+
{{exitem|di=outputfbk|ex=7.12|ti=Whipple bicycle model|fi=bicycle-whipple.tex|st=|au=|co=|re=}}
{{exitem|di=outputfbk|ex=13|ti=Discrete-time random walk|fi=kalman-randomwalk.tex|st=P|au=|co=|re=}}
+
{{exitem|di=outputfbk|ex=7.13|ti=Discrete-time random walk|fi=kalman-randomwalk.tex|st=P|au=|co=|re=}}
{{exitem|di=outputfbk|ex=14|ti=Kalman decomposition|fi=missing|st=|au=|co=|re=}}
+
{{exitem|di=outputfbk|ex=7.14|ti=Kalman decomposition|fi=missing|st=|au=|co=|re=}}
{{exitem|di=outputfbk|ex=15|ti=|fi=missing|st=|au=|co=|re=}}
+
{{exitem|di=outputfbk|ex=7.15|ti=|fi=missing|st=|au=|co=|re=}}
{{exitem|di=outputfbk|ex=16|ti=Balance system|fi=balance-observable.tex|st=|au=|co=|re=}}
+
{{exitem|di=outputfbk|ex=7.16|ti=Balance system|fi=balance-observable.tex|st=|au=|co=|re=}}
{{exitem|di=outputfbk|ex=17|ti=Balance system with biased measurement|fi=balance-statectrl.tex|st=|au=|co=|re=}}
+
{{exitem|di=outputfbk|ex=7.17|ti=Balance system with biased measurement|fi=balance-statectrl.tex|st=|au=|co=|re=}}
{{exitem|di=outputfbk|ex=18|ti=Duality|fi=missing|st=|au=|co=|re=}}
+
{{exitem|di=outputfbk|ex=7.18|ti=Duality|fi=missing|st=|au=|co=|re=}}
{{exitem|di=outputfbk|ex=19|ti=Balance system|fi=missing|st=|au=|co=|re=}}
+
{{exitem|di=outputfbk|ex=7.19|ti=Balance system|fi=missing|st=|au=|co=|re=}}
{{exitem|di=outputfbk|ex=20|ti=Trajectory generation|fi=trajgen-scalar.tex|st=|au=|co=|re=}}
+
{{exitem|di=outputfbk|ex=7.20|ti=Trajectory generation|fi=trajgen-scalar.tex|st=|au=|co=|re=}}
{{exitem|di=outputfbk|ex=21|ti=Selection of eigenvalues|fi=missing|st=|au=|co=|re=}}
+
{{exitem|di=outputfbk|ex=7.21|ti=Selection of eigenvalues|fi=missing|st=|au=|co=|re=}}
{{exitem|di=outputfbk|ex=22|ti=Kalman filter for scalar ODE|fi=kalman-scalar.tex|st=P|au=|co=|re=}}
+
{{exitem|di=outputfbk|ex=7.22|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=xferfcns|ex=1|ti=|fi=missing|st=|au=|co=|re=}}
+
{{exitem|di=xferfcns|ex=8.1|ti=|fi=missing|st=|au=|co=|re=}}
{{exitem|di=xferfcns|ex=2|ti=|fi=modalinput.tex|st=P|au=|co=|re=}}
+
{{exitem|di=xferfcns|ex=8.2|ti=|fi=modalinput.tex|st=P|au=|co=|re=}}
{{exitem|di=xferfcns|ex=3|ti=Inverted pendulum|fi=invpend-xferfcn.tex|st=P|au=|co=|re=}}
+
{{exitem|di=xferfcns|ex=8.3|ti=Inverted pendulum|fi=invpend-xferfcn.tex|st=P|au=|co=|re=}}
{{exitem|di=xferfcns|ex=4|ti=Solutions corresponding to poles and zeros|fi=missing|st=P|au=|co=|re=}}
+
{{exitem|di=xferfcns|ex=8.4|ti=Solutions corresponding to poles and zeros|fi=missing|st=P|au=|co=|re=}}
{{exitem|di=xferfcns|ex=5|ti=Operational amplifier|fi=opamp-pictrl.tex|st=P|au=|co=|re=}}
+
{{exitem|di=xferfcns|ex=8.5|ti=Operational amplifier|fi=opamp-pictrl.tex|st=P|au=|co=|re=}}
{{exitem|di=xferfcns|ex=6|ti=Transfer function for state space system|fi=missing|st=P|au=|co=|re=}}
+
{{exitem|di=xferfcns|ex=8.6|ti=Transfer function for state space system|fi=missing|st=P|au=|co=|re=}}
{{exitem|di=xferfcns|ex=7|ti=Kalman decomposition|fi=missing|st=|au=|co=|re=}}
+
{{exitem|di=xferfcns|ex=8.7|ti=Kalman decomposition|fi=missing|st=|au=|co=|re=}}
{{exitem|di=xferfcns|ex=8|ti=|fi=missing|st=|au=|co=|re=}}
+
{{exitem|di=xferfcns|ex=8.8|ti=|fi=missing|st=|au=|co=|re=}}
{{exitem|di=xferfcns|ex=9|ti=Bode plot for a simple zero|fi=missing|st=|au=|co=|re=}}
+
{{exitem|di=xferfcns|ex=8.9|ti=Bode plot for a simple zero|fi=missing|st=|au=|co=|re=}}
{{exitem|di=xferfcns|ex=10|ti=Vectored thrust aircraft|fi=pvtol-lateraltf.tex|st=P|au=|co=|re=}}
+
{{exitem|di=xferfcns|ex=8.10|ti=Vectored thrust aircraft|fi=pvtol-lateraltf.tex|st=P|au=|co=|re=}}
{{exitem|di=xferfcns|ex=11|ti=Common poles|fi=missing|st=|au=|co=|re=}}
+
{{exitem|di=xferfcns|ex=8.11|ti=Common poles|fi=missing|st=|au=|co=|re=}}
{{exitem|di=xferfcns|ex=12|ti=Congestion control|fi=congctrl-xferfcns.tex|st=P|au=|co=|re=}}
+
{{exitem|di=xferfcns|ex=8.12|ti=Congestion control|fi=congctrl-xferfcns.tex|st=P|au=|co=|re=}}
{{exitem|di=xferfcns|ex=13|ti=Inverted pendulum with PD control|fi=invpend-pzcancel.tex|st=P|au=|co=|re=}}
+
{{exitem|di=xferfcns|ex=8.13|ti=Inverted pendulum with PD control|fi=invpend-pzcancel.tex|st=P|au=|co=|re=}}
{{exitem|di=xferfcns|ex=14|ti=Vehicle suspension~\cite{hedrick90}|fi=vehicle-quartercar.tex|st=|au=|co=|re=}}
+
{{exitem|di=xferfcns|ex=8.14|ti=Vehicle suspension~\cite{hedrick90}|fi=vehicle-quartercar.tex|st=|au=|co=|re=}}
{{exitem|di=xferfcns|ex=15|ti=Vibration absorber|fi=missing|st=P|au=|co=|re=}}
+
{{exitem|di=xferfcns|ex=8.15|ti=Vibration absorber|fi=missing|st=P|au=|co=|re=}}
{{exitem|di=xferfcns|ex=16|ti=|fi=freqexamps.tex|st=P|au=|co=|re=}}
+
{{exitem|di=xferfcns|ex=8.16|ti=|fi=freqexamps.tex|st=P|au=|co=|re=}}
{{exitem|di=xferfcns|ex=17|ti=|fi=model-simplification.tex|st=|au=|co=|re=}}
+
{{exitem|di=xferfcns|ex=8.17|ti=|fi=model-simplification.tex|st=|au=|co=|re=}}
{{exitem|di=xferfcns|ex=18|ti=|fi=cruise-pictrl.tex|st=P|au=|co=|re=}}
+
{{exitem|di=xferfcns|ex=8.18|ti=|fi=cruise-pictrl.tex|st=P|au=|co=|re=}}
{{exitem|di=xferfcns|ex=19|ti=|fi=dcmotor-xferfcn.tex|st=|au=|co=|re=}}
+
{{exitem|di=xferfcns|ex=8.19|ti=|fi=dcmotor-xferfcn.tex|st=|au=|co=|re=}}
{{exitem|di=xferfcns|ex=20|ti=|fi=missing|st=|au=|co=|re=}}
+
{{exitem|di=xferfcns|ex=8.20|ti=|fi=missing|st=|au=|co=|re=}}
{{exitem|di=xferfcns|ex=21|ti=|fi=missing|st=P|au=|co=|re=}}
+
{{exitem|di=xferfcns|ex=8.21|ti=|fi=missing|st=P|au=|co=|re=}}
{{exitem|di=xferfcns|ex=22|ti=|fi=missing|st=|au=|co=|re=}}
+
{{exitem|di=xferfcns|ex=8.22|ti=|fi=missing|st=|au=|co=|re=}}
{{exitem|di=xferfcns|ex=23|ti=|fi=missing|st=|au=|co=|re=}}
+
{{exitem|di=xferfcns|ex=8.23|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=loopanal|ex=1|ti=Operational amplifier|fi=opamp-unitygain.tex|st=P|au=|co=|re=}}
+
{{exitem|di=loopanal|ex=9.1|ti=Operational amplifier|fi=opamp-unitygain.tex|st=P|au=|co=|re=}}
{{exitem|di=loopanal|ex=2|ti=Atomic force microscope|fi=afm-tapping.tex|st=|au=|co=|re=}}
+
{{exitem|di=loopanal|ex=9.2|ti=Atomic force microscope|fi=afm-tapping.tex|st=|au=|co=|re=}}
{{exitem|di=loopanal|ex=3|ti=Heat conduction|fi=missing|st=P|au=|co=|re=}}
+
{{exitem|di=loopanal|ex=9.3|ti=Heat conduction|fi=missing|st=P|au=|co=|re=}}
{{exitem|di=loopanal|ex=4|ti=Vectored thrust aircraft|fi=pvtol-looptf.tex|st=P|au=|co=|re=}}
+
{{exitem|di=loopanal|ex=9.4|ti=Vectored thrust aircraft|fi=pvtol-looptf.tex|st=P|au=|co=|re=}}
{{exitem|di=loopanal|ex=5|ti=Vehicle steering|fi=missing|st=|au=|co=|re=}}
+
{{exitem|di=loopanal|ex=9.5|ti=Vehicle steering|fi=missing|st=|au=|co=|re=}}
{{exitem|di=loopanal|ex=6|ti=Stability margins for second-order systems|fi=missing|st=P|au=|co=|re=}}
+
{{exitem|di=loopanal|ex=9.6|ti=Stability margins for second-order systems|fi=missing|st=P|au=|co=|re=}}
{{exitem|di=loopanal|ex=7|ti=Congestion control in overload conditions|fi=congctrl-overload.tex|st=P|au=|co=|re=}}
+
{{exitem|di=loopanal|ex=9.7|ti=Congestion control in overload conditions|fi=congctrl-overload.tex|st=P|au=|co=|re=}}
{{exitem|di=loopanal|ex=8|ti=Bode's formula|fi=missing|st=|au=|co=|re=}}
+
{{exitem|di=loopanal|ex=9.8|ti=Bode's formula|fi=missing|st=|au=|co=|re=}}
{{exitem|di=loopanal|ex=9|ti=Pad\'e approximation to a time delay|fi=missing|st=|au=|co=|re=}}
+
{{exitem|di=loopanal|ex=9.9|ti=Pad\'e approximation to a time delay|fi=missing|st=|au=|co=|re=}}
{{exitem|di=loopanal|ex=10|ti=Inverse response|fi=missing|st=P|au=|co=|re=}}
+
{{exitem|di=loopanal|ex=9.10|ti=Inverse response|fi=missing|st=P|au=|co=|re=}}
{{exitem|di=loopanal|ex=11|ti=Describing function analysis|fi=missing|st=|au=|co=|re=}}
+
{{exitem|di=loopanal|ex=9.11|ti=Describing function analysis|fi=missing|st=|au=|co=|re=}}
{{exitem|di=loopanal|ex=12|ti=Right half-plane pole|fi=missing|st=P|au=|co=|re=}}
+
{{exitem|di=loopanal|ex=9.12|ti=Right half-plane pole|fi=missing|st=P|au=|co=|re=}}
{{exitem|di=loopanal|ex=13|ti=Third-order system|fi=missing|st=|au=|co=|re=}}
+
{{exitem|di=loopanal|ex=9.13|ti=Third-order system|fi=missing|st=|au=|co=|re=}}
{{exitem|di=loopanal|ex=14|ti=|fi=bodenyq.tex|st=P|au=|co=|re=}}
+
{{exitem|di=loopanal|ex=9.14|ti=|fi=bodenyq.tex|st=P|au=|co=|re=}}
{{exitem|di=loopanal|ex=15|ti=Congestion control using TCP/Reno|fi=congctrl-margins.tex|st=|au=|co=|re=}}
+
{{exitem|di=loopanal|ex=9.15|ti=Congestion control using TCP/Reno|fi=congctrl-margins.tex|st=|au=|co=|re=}}
{{exitem|di=loopanal|ex=16|ti=|fi=opamp-routh.tex|st=P|au=|co=|re=}}
+
{{exitem|di=loopanal|ex=9.16|ti=|fi=opamp-routh.tex|st=P|au=|co=|re=}}
{{exitem|di=loopanal|ex=17|ti=|fi=missing|st=P|au=|co=|re=}}
+
{{exitem|di=loopanal|ex=9.17|ti=|fi=missing|st=P|au=|co=|re=}}
{{exitem|di=loopanal|ex=18|ti=Limitations|fi=missing|st=|au=|co=|re=}}
+
{{exitem|di=loopanal|ex=9.18|ti=Limitations|fi=missing|st=|au=|co=|re=}}
{{exitem|di=loopanal|ex=19|ti=Limitations|fi=missing|st=|au=|co=|re=}}
+
{{exitem|di=loopanal|ex=9.19|ti=Limitations|fi=missing|st=|au=|co=|re=}}
{{exitem|di=loopanal|ex=20|ti=Delay differential equations|fi=delayde.tex|st=P|au=|co=|re=}}
+
{{exitem|di=loopanal|ex=9.20|ti=Delay differential equations|fi=delayde.tex|st=P|au=|co=|re=}}
{{exitem|di=loopanal|ex=21|ti=Cruise control design|fi=cruise-pictrl.tex|st=P|au=|co=|re=}}
+
{{exitem|di=loopanal|ex=9.21|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=pid|ex=1|ti=Ideal PID controllers|fi=missing|st=|au=|co=|re=}}
+
{{exitem|di=pid|ex=10.1|ti=Ideal PID controllers|fi=missing|st=|au=|co=|re=}}
{{exitem|di=pid|ex=2|ti=|fi=missing|st=|au=|co=|re=}}
+
{{exitem|di=pid|ex=10.2|ti=|fi=missing|st=|au=|co=|re=}}
{{exitem|di=pid|ex=3|ti=|fi=missing|st=P|au=|co=|re=}}
+
{{exitem|di=pid|ex=10.3|ti=|fi=missing|st=P|au=|co=|re=}}
{{exitem|di=pid|ex=4|ti=Ziegler--Nichols tuning|fi=missing|st=P|au=|co=|re=}}
+
{{exitem|di=pid|ex=10.4|ti=Ziegler--Nichols tuning|fi=missing|st=P|au=|co=|re=}}
{{exitem|di=pid|ex=5|ti=Vehicle steering|fi=steering-pi.tex|st=P|au=|co=|re=}}
+
{{exitem|di=pid|ex=10.5|ti=Vehicle steering|fi=steering-pi.tex|st=P|au=|co=|re=}}
{{exitem|di=pid|ex=6|ti=Congestion control|fi=congctrl-pituning.tex|st=P|au=|co=|re=}}
+
{{exitem|di=pid|ex=10.6|ti=Congestion control|fi=congctrl-pituning.tex|st=P|au=|co=|re=}}
{{exitem|di=pid|ex=7|ti=Motor drive|fi=dcmotor-pdctrl.tex|st=P|au=|co=|re=}}
+
{{exitem|di=pid|ex=10.7|ti=Motor drive|fi=dcmotor-pdctrl.tex|st=P|au=|co=|re=}}
{{exitem|di=pid|ex=8|ti=|fi=missing|st=|au=|co=|re=}}
+
{{exitem|di=pid|ex=10.8|ti=|fi=missing|st=|au=|co=|re=}}
{{exitem|di=pid|ex=9|ti=Tuning rules|fi=missing|st=P|au=|co=|re=}}
+
{{exitem|di=pid|ex=10.9|ti=Tuning rules|fi=missing|st=P|au=|co=|re=}}
{{exitem|di=pid|ex=10|ti=Windup and anti-windup|fi=missing|st=|au=|co=|re=}}
+
{{exitem|di=pid|ex=10.10|ti=Windup and anti-windup|fi=missing|st=|au=|co=|re=}}
{{exitem|di=pid|ex=11|ti=Windup protection by conditional integration|fi=missing|st=P|au=|co=|re=}}
+
{{exitem|di=pid|ex=10.11|ti=Windup protection by conditional integration|fi=missing|st=P|au=|co=|re=}}
{{exitem|di=pid|ex=12|ti=|fi=pidmethods.tex|st=P|au=|co=|re=}}
+
{{exitem|di=pid|ex=10.12|ti=|fi=pidmethods.tex|st=P|au=|co=|re=}}
{{exitem|di=pid|ex=13|ti=|fi=pidexmps.tex|st=P|au=|co=|re=}}
+
{{exitem|di=pid|ex=10.13|ti=|fi=pidexmps.tex|st=P|au=|co=|re=}}
{{exitem|di=pid|ex=14|ti=Compartment model|fi=compartment-monotone.tex|st=|au=|co=|re=}}
+
{{exitem|di=pid|ex=10.14|ti=Compartment model|fi=compartment-monotone.tex|st=|au=|co=|re=}}
{{exitem|di=pid|ex=15|ti=|fi=missing|st=P|au=|co=|re=}}
+
{{exitem|di=pid|ex=10.15|ti=|fi=missing|st=P|au=|co=|re=}}
{{exitem|di=pid|ex=16|ti=|fi=pirlocus.tex|st=P|au=|co=|re=}}
+
{{exitem|di=pid|ex=10.16|ti=|fi=pirlocus.tex|st=P|au=|co=|re=}}
{{exitem|di=pid|ex=17|ti=|fi=pvtol-pid.tex|st=P|au=|co=|re=}}
+
{{exitem|di=pid|ex=10.17|ti=|fi=pvtol-pid.tex|st=P|au=|co=|re=}}
{{exitem|di=pid|ex=18|ti=Ball and beam|fi=missing|st=|au=|co=|re=}}
+
{{exitem|di=pid|ex=10.18|ti=Ball and beam|fi=missing|st=|au=|co=|re=}}
{{exitem|di=pid|ex=19|ti=|fi=balance-pid.tex|st=P|au=|co=|re=}}
+
{{exitem|di=pid|ex=10.19|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=loopsyn|ex=1|ti=|fi=missing|st=|au=|co=|re=}}
+
{{exitem|di=loopsyn|ex=11.1|ti=|fi=missing|st=|au=|co=|re=}}
{{exitem|di=loopsyn|ex=2|ti=|fi=missing|st=|au=|co=|re=}}
+
{{exitem|di=loopsyn|ex=11.2|ti=|fi=missing|st=|au=|co=|re=}}
{{exitem|di=loopsyn|ex=3|ti=|fi=missing|st=P|au=|co=|re=}}
+
{{exitem|di=loopsyn|ex=11.3|ti=|fi=missing|st=P|au=|co=|re=}}
{{exitem|di=loopsyn|ex=4|ti=|fi=missing|st=|au=|co=|re=}}
+
{{exitem|di=loopsyn|ex=11.4|ti=|fi=missing|st=|au=|co=|re=}}
{{exitem|di=loopsyn|ex=5|ti=Sensitivity of feedback and feedforward|fi=missing|st=|au=|co=|re=}}
+
{{exitem|di=loopsyn|ex=11.5|ti=Sensitivity of feedback and feedforward|fi=missing|st=|au=|co=|re=}}
{{exitem|di=loopsyn|ex=6|ti=Equivalence of controllers with two degrees of freedom|fi=missing|st=|au=|co=|re=}}
+
{{exitem|di=loopsyn|ex=11.6|ti=Equivalence of controllers with two degrees of freedom|fi=missing|st=|au=|co=|re=}}
{{exitem|di=loopsyn|ex=7|ti=Disturbance attenuation|fi=missing|st=|au=|co=|re=}}
+
{{exitem|di=loopsyn|ex=11.7|ti=Disturbance attenuation|fi=missing|st=|au=|co=|re=}}
{{exitem|di=loopsyn|ex=8|ti=Disturbance reduction through feedback|fi=missing|st=P|au=|co=|re=}}
+
{{exitem|di=loopsyn|ex=11.8|ti=Disturbance reduction through feedback|fi=missing|st=P|au=|co=|re=}}
{{exitem|di=loopsyn|ex=9|ti=|fi=missing|st=|au=|co=|re=}}
+
{{exitem|di=loopsyn|ex=11.9|ti=|fi=missing|st=|au=|co=|re=}}
{{exitem|di=loopsyn|ex=10|ti=Attenuation of low-frequency sinusoidal disturbances|fi=missing|st=P|au=|co=|re=}}
+
{{exitem|di=loopsyn|ex=11.10|ti=Attenuation of low-frequency sinusoidal disturbances|fi=missing|st=P|au=|co=|re=}}
{{exitem|di=loopsyn|ex=11|ti=|fi=missing|st=|au=|co=|re=}}
+
{{exitem|di=loopsyn|ex=11.11|ti=|fi=missing|st=|au=|co=|re=}}
{{exitem|di=loopsyn|ex=12|ti=|fi=missing|st=P|au=|co=|re=}}
+
{{exitem|di=loopsyn|ex=11.12|ti=|fi=missing|st=P|au=|co=|re=}}
{{exitem|di=loopsyn|ex=13|ti=|fi=missing|st=P|au=|co=|re=}}
+
{{exitem|di=loopsyn|ex=11.13|ti=|fi=missing|st=P|au=|co=|re=}}
{{exitem|di=loopsyn|ex=14|ti=Phase margin formulas|fi=missing|st=|au=|co=|re=}}
+
{{exitem|di=loopsyn|ex=11.14|ti=Phase margin formulas|fi=missing|st=|au=|co=|re=}}
{{exitem|di=loopsyn|ex=15|ti=|fi=balance-visual.tex|st=P|au=|co=|re=}}
+
{{exitem|di=loopsyn|ex=11.15|ti=|fi=balance-visual.tex|st=P|au=|co=|re=}}
{{exitem|di=loopsyn|ex=16|ti=Rear-steered bicycle|fi=bicycle-rearsteer.tex|st=P|au=|co=|re=}}
+
{{exitem|di=loopsyn|ex=11.16|ti=Rear-steered bicycle|fi=bicycle-rearsteer.tex|st=P|au=|co=|re=}}
{{exitem|di=loopsyn|ex=17|ti=|fi=missing|st=P|au=|co=|re=}}
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{{exitem|di=loopsyn|ex=11.17|ti=|fi=missing|st=P|au=|co=|re=}}
{{exitem|di=loopsyn|ex=18|ti=Rise-time/bandwidth product|fi=missing|st=|au=|co=|re=}}
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{{exitem|di=loopsyn|ex=11.18|ti=Rise-time/bandwidth product|fi=missing|st=|au=|co=|re=}}
{{exitem|di=loopsyn|ex=19|ti=|fi=missing|st=P|au=|co=|re=}}
+
{{exitem|di=loopsyn|ex=11.19|ti=|fi=missing|st=P|au=|co=|re=}}
{{exitem|di=loopsyn|ex=20|ti=|fi=znlimits.tex|st=|au=|co=|re=}}
+
{{exitem|di=loopsyn|ex=11.20|ti=|fi=znlimits.tex|st=|au=|co=|re=}}
{{exitem|di=loopsyn|ex=21|ti=Pole in the right half-plane and time delay|fi=missing|st=P|au=|co=|re=}}
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{{exitem|di=loopsyn|ex=11.21|ti=Pole in the right half-plane and time delay|fi=missing|st=P|au=|co=|re=}}
{{exitem|di=loopsyn|ex=22|ti=Cancellation of unstable process zero|fi=missing|st=|au=|co=|re=}}
+
{{exitem|di=loopsyn|ex=11.22|ti=Cancellation of unstable process zero|fi=missing|st=|au=|co=|re=}}
{{exitem|di=loopsyn|ex=23|ti=Limitations on achievable phase lag|fi=missing|st=P|au=|co=|re=}}
+
{{exitem|di=loopsyn|ex=11.23|ti=Limitations on achievable phase lag|fi=missing|st=P|au=|co=|re=}}
{{exitem|di=loopsyn|ex=24|ti=|fi=missing|st=|au=|co=|re=}}
+
{{exitem|di=loopsyn|ex=11.24|ti=|fi=missing|st=|au=|co=|re=}}
{{exitem|di=loopsyn|ex=25|ti=Performance characteristics of second-order systems|fi=secord-perf.tex|st=P|au=|co=|re=}}
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{{exitem|di=loopsyn|ex=11.25|ti=Performance characteristics of second-order systems|fi=secord-perf.tex|st=P|au=|co=|re=}}
{{exitem|di=loopsyn|ex=26|ti=|fi=secord-rhpz.tex|st=P|au=|co=|re=}}
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{{exitem|di=loopsyn|ex=11.26|ti=|fi=secord-rhpz.tex|st=P|au=|co=|re=}}
{{exitem|di=loopsyn|ex=27|ti=Integral of complementary sensitivity|fi=missing|st=P|au=|co=|re=}}
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{{exitem|di=loopsyn|ex=11.27|ti=Integral of complementary sensitivity|fi=missing|st=P|au=|co=|re=}}
{{exitem|di=loopsyn|ex=28|ti=Bode's integral|fi=missing|st=P|au=|co=|re=}}
+
{{exitem|di=loopsyn|ex=11.28|ti=Bode's integral|fi=missing|st=P|au=|co=|re=}}
{{exitem|di=loopsyn|ex=29|ti=Lead compensator for an insect flight control system|fi=flylead.tex|st=P|au=|co=|re=}}
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{{exitem|di=loopsyn|ex=11.29|ti=Lead compensator for an insect flight control system|fi=flylead.tex|st=P|au=|co=|re=}}
{{exitem|di=loopsyn|ex=30|ti=Control of a magnetic levitation system|fi=maglev.tex|st=P|au=|co=|re=}}
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{{exitem|di=loopsyn|ex=11.30|ti=Control of a magnetic levitation system|fi=maglev.tex|st=P|au=|co=|re=}}
{{exitem|di=loopsyn|ex=31|ti=|fi=missing|st=P|au=|co=|re=}}
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{{exitem|di=loopsyn|ex=11.31|ti=|fi=missing|st=P|au=|co=|re=}}
{{exitem|di=loopsyn|ex=32|ti=|fi=pvtol-gangof4.tex|st=|au=|co=|re=}}
+
{{exitem|di=loopsyn|ex=11.32|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=robperf|ex=1|ti=|fi=missing|st=P|au=|co=|re=}}
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{{exitem|di=robperf|ex=12.1|ti=|fi=missing|st=P|au=|co=|re=}}
{{exitem|di=robperf|ex=2|ti=|fi=missing|st=P|au=|co=|re=}}
+
{{exitem|di=robperf|ex=12.2|ti=|fi=missing|st=P|au=|co=|re=}}
{{exitem|di=robperf|ex=3|ti=Difference in sensitivity functions|fi=missing|st=P|au=|co=|re=}}
+
{{exitem|di=robperf|ex=12.3|ti=Difference in sensitivity functions|fi=missing|st=P|au=|co=|re=}}
{{exitem|di=robperf|ex=4|ti=The Riemann sphere|fi=missing|st=P|au=|co=|re=}}
+
{{exitem|di=robperf|ex=12.4|ti=The Riemann sphere|fi=missing|st=P|au=|co=|re=}}
{{exitem|di=robperf|ex=5|ti=Stability margins|fi=missing|st=|au=|co=|re=}}
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{{exitem|di=robperf|ex=12.5|ti=Stability margins|fi=missing|st=|au=|co=|re=}}
{{exitem|di=robperf|ex=6|ti=Bode's ideal loop transfer function|fi=missing|st=P|au=|co=|re=}}
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{{exitem|di=robperf|ex=12.6|ti=Bode's ideal loop transfer function|fi=missing|st=P|au=|co=|re=}}
{{exitem|di=robperf|ex=7|ti=|fi=missing|st=P|au=|co=|re=}}
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{{exitem|di=robperf|ex=12.7|ti=|fi=missing|st=P|au=|co=|re=}}
{{exitem|di=robperf|ex=8|ti=Smith predictor|fi=missing|st=|au=|co=|re=}}
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{{exitem|di=robperf|ex=12.8|ti=Smith predictor|fi=missing|st=|au=|co=|re=}}
{{exitem|di=robperf|ex=9|ti=Ideal delay compensator|fi=missing|st=|au=|co=|re=}}
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{{exitem|di=robperf|ex=12.9|ti=Ideal delay compensator|fi=missing|st=|au=|co=|re=}}
{{exitem|di=robperf|ex=10|ti=Vehicle steering|fi=missing|st=|au=|co=|re=}}
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{{exitem|di=robperf|ex=12.10|ti=Vehicle steering|fi=missing|st=|au=|co=|re=}}
{{exitem|di=robperf|ex=11|ti=|fi=missing|st=|au=|co=|re=}}
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{{exitem|di=robperf|ex=12.11|ti=|fi=missing|st=|au=|co=|re=}}
{{exitem|di=robperf|ex=12|ti=AFM nanopositioning system|fi=missing|st=|au=|co=|re=}}
+
{{exitem|di=robperf|ex=12.12|ti=AFM nanopositioning system|fi=missing|st=|au=|co=|re=}}
{{exitem|di=robperf|ex=13|ti=$H_\infty$ control|fi=missing|st=|au=|co=|re=}}
+
{{exitem|di=robperf|ex=12.13|ti=$H_\infty$ control|fi=missing|st=|au=|co=|re=}}
{{exitem|di=robperf|ex=14|ti=|fi=missing|st=|au=|co=|re=}}
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{{exitem|di=robperf|ex=12.14|ti=|fi=missing|st=|au=|co=|re=}}
{{exitem|di=robperf|ex=15|ti=|fi=missing|st=P|au=|co=|re=}}
+
{{exitem|di=robperf|ex=12.15|ti=|fi=missing|st=P|au=|co=|re=}}
{{exitem|di=robperf|ex=16|ti=Robustness using the Nyquist criterion|fi=missing|st=P|au=|co=|re=}}
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{{exitem|di=robperf|ex=12.16|ti=Robustness using the Nyquist criterion|fi=missing|st=P|au=|co=|re=}}
{{exitem|di=robperf|ex=17|ti=Robustness inequalities|fi=missing|st=|au=|co=|re=}}
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{{exitem|di=robperf|ex=12.17|ti=Robustness inequalities|fi=missing|st=|au=|co=|re=}}
{{exitem|di=robperf|ex=18|ti=|fi=missing|st=|au=|co=|re=}}
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{{exitem|di=robperf|ex=12.18|ti=|fi=missing|st=|au=|co=|re=}}
{{exitem|di=robperf|ex=19|ti=|fi=missing|st=|au=|co=|re=}}
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{{exitem|di=robperf|ex=12.19|ti=|fi=missing|st=|au=|co=|re=}}
{{exitem|di=robperf|ex=20|ti=Disk drive tracking|fi=missing|st=|au=|co=|re=}}
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{{exitem|di=robperf|ex=12.20|ti=Disk drive tracking|fi=missing|st=|au=|co=|re=}}
 
{{exercise table end}}
 
{{exercise table end}}

Revision as of 19:07, 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
2.1 Chain of integrators form chainofint.tex
2.2 Inverted pendulum balance-bal2inv.tex P
2.3 Disrete-time dynamics discrete-solutions.tex P
2.4 Keynesian economics discrete-keynes.tex
2.5 Least squares system identification sysid-leastsq.tex
2.6 Normalized oscillator dynamics oscillator.tex P
2.7 Electric generator powergrid.tex P
2.8 Admission control for a queue queue-admcontrol.tex P
2.9 Biological switch biocircuits-switchmod.tex P
2.10 Motor drive dcmotor-modeling.tex P
2.11 Uncertainty lemon lemon.tex P
2.12 Frequency response freqresp.tex
2.13 Eye and head motion occular-blockdiag.tex P
2.14 Second-order system identification sysid-logdec.tex
2.15 Insect vision flyvision.tex P
2.16 State space model for balance systems balance-statespace.tex
2.17 fingerflame.tex P
2.18 Consensus and invariants compsys-invariants.tex P
2.19 Electric motor electricmotor.tex P
2.20 exothermic.tex
2.21 caffeine.tex P
2.22 ballbeam-modeling.tex P
2.23 pvtol2invpend.tex
2.24 flyflight.tex
2.25 pendulum.tex P

Chapter 3 - Examples

Num Title Filename Stat Auth Comments
3.1 Cruise control cruise-hillsim.tex
3.2 Bicycle dynamics bicycle-statespace.tex
3.3 Bicycle steering bicycle-steering.tex
3.4 Operational amplifier circuit opamp-twopole.tex P
3.5 Operational amplifier oscillator opamp-osc.tex P
3.6 Congestion control using RED~\cite{Low+02:infocom} congctrl-red.tex P
3.7 Atomic force microscope with piezo tube afm-preload.tex P
3.8 Drug administration drugadmin-alcohol.tex
3.9 Population dynamics logistic.tex
3.10 Fisheries management fishery-modeling.tex P
3.11 powertrain.tex P

Chapter 4 - Dynamic Behavior

Num Title Filename Stat Auth Comments
4.1 Time-invariant systems timeshift.tex
4.2 Flow in a tank tank-modeling.tex P
4.3 Cruise control cruise-phaseplot.tex P
4.4 Lyapunov functions lyap-secord.tex P
4.5 Damped spring--mass system lyap-oscillator.tex P
4.6 Electric generator missing P
4.7 Lyapunov equation missing
4.8 Congestion control congctrl-lyapstab.tex P
4.9 Swinging up a pendulum invpend-swingup.tex P
4.10 Root locus diagram missing P
4.11 Discrete-time Lyapunov function discrete-lyapunov.tex
4.12 Operational amplifier oscillator opamp-oscnl.tex P
4.13 Self-activating genetic circuit biocircuits-posfbk.tex P
4.14 Diagonal systems missing P
4.15 Furuta pendulum furuta.tex P
4.16 Routh-Hurwitz criterion routh.tex
4.17 missing
4.18 missing P
4.19 predprey-limit.tex P
4.20 Windup protection by conditional integration missing P
4.21 missing
4.22 Spike generation in neurons missing P
4.23 compsys-consensus.tex
4.24 Steering dynamics of a ship tanker-dynamics.tex P
4.25 Pitchfork bifurcation missing
4.26 stabexmp-mooregreitzer.tex P
4.27 cruise-lyapunov.tex P
4.28 lyapexmp.tex P

Chapter 5 - Linear Systems

Num Title Filename Stat Auth Comments
5.1 Response to the derivative of a signal missing
5.2 Impulse response and convolution missing
5.3 Pulse response for a compartment model compartment-pulse.tex
5.4 Matrix exponential for second-order system matrixexp.tex P
5.5 Lyapunov function for a linear system missing
5.6 Nondiagonal Jordan form missing P
5.7 Rise time for a first-order system missing
5.8 Discrete-time systems discrete-linsys.tex P
5.9 Keynesian economics discrete-keynes.tex
5.10 missing P
5.11 Transcriptional regulation biocircuits-negfbk.tex P
5.12 Normalized coordinates for second-order system missing
5.13 Matrix exponential for Jordan form missing
5.14 Solution of a second-order system missing
5.15 Monotone step response missing
5.16 missing P
5.17 missing P
5.18 linexmp-coupled.tex P
5.19 State variables in compartment models compartment-states.tex
5.20 queue-linsys.tex P
5.21 Keynes model in continuous time missing
5.22 cartpend.tex P
5.23 missing P

Chapter 6 - State Feedback

Num Title Filename Stat Auth Comments
6.1 Double integrator missing P
6.2 Reachability from nonzero initial state missing
6.3 Unreachable systems missing
6.4 Integral feedback for rejecting constant disturbances missing
6.5 Rear-steered bicycle bicycle-rearsteer.tex P
6.6 Characteristic polynomial for reachable canonical form missing
6.7 Reachability matrix for reachable canonical form missing P
6.8 Non-maintainable equilibria missing P
6.9 Eigenvalue assignment for unreachable system missing P
6.10 Cayley--Hamilton theorem missing
6.11 Motor drive missing
6.12 Whipple bicycle model bicycle-whipple.tex P
6.13 Atomic force microscope missing
6.14 missing P
6.15 Bryson's rule brysons-rule.tex
6.16 integral-refgain.tex
6.17 Unreachable compartment model compartment-nonreach.tex P
6.18 missing
6.19 missing

Chapter 7 - Output Feedback

Num Title Filename Stat Auth Comments
7.1 Coordinate transformations missing
7.2 missing
7.3 Observable canonical form missing
7.4 Bicycle dynamics bicycle-observability.tex P
7.5 Integral action integral-action.tex P
7.6 Vectored thrust aircraft pvtol-ssctrl.tex P
7.7 Uniqueness of observers missing
7.8 Observers using differentiation diff.tex
7.9 Observer for Teorell's compartment model compartment-teorellobs.tex P
7.10 Observer design for motor drive dcmotor-observer.tex P
7.11 Feedforward design for motor drive dcmotor-feedforward.tex P
7.12 Whipple bicycle model bicycle-whipple.tex
7.13 Discrete-time random walk kalman-randomwalk.tex P
7.14 Kalman decomposition missing
7.15 missing
7.16 Balance system balance-observable.tex
7.17 Balance system with biased measurement balance-statectrl.tex
7.18 Duality missing
7.19 Balance system missing
7.20 Trajectory generation trajgen-scalar.tex
7.21 Selection of eigenvalues missing
7.22 Kalman filter for scalar ODE kalman-scalar.tex P

Chapter 8 - Transfer Functions

Num Title Filename Stat Auth Comments
8.1 missing
8.2 modalinput.tex P
8.3 Inverted pendulum invpend-xferfcn.tex P
8.4 Solutions corresponding to poles and zeros missing P
8.5 Operational amplifier opamp-pictrl.tex P
8.6 Transfer function for state space system missing P
8.7 Kalman decomposition missing
8.8 missing
8.9 Bode plot for a simple zero missing
8.10 Vectored thrust aircraft pvtol-lateraltf.tex P
8.11 Common poles missing
8.12 Congestion control congctrl-xferfcns.tex P
8.13 Inverted pendulum with PD control invpend-pzcancel.tex P
8.14 Vehicle suspension~\cite{hedrick90} vehicle-quartercar.tex
8.15 Vibration absorber missing P
8.16 freqexamps.tex P
8.17 model-simplification.tex
8.18 cruise-pictrl.tex P
8.19 dcmotor-xferfcn.tex
8.20 missing
8.21 missing P
8.22 missing
8.23 missing

Chapter 9 - Frequency Domain Analysis

Num Title Filename Stat Auth Comments
9.1 Operational amplifier opamp-unitygain.tex P
9.2 Atomic force microscope afm-tapping.tex
9.3 Heat conduction missing P
9.4 Vectored thrust aircraft pvtol-looptf.tex P
9.5 Vehicle steering missing
9.6 Stability margins for second-order systems missing P
9.7 Congestion control in overload conditions congctrl-overload.tex P
9.8 Bode's formula missing
9.9 Pad\'e approximation to a time delay missing
9.10 Inverse response missing P
9.11 Describing function analysis missing
9.12 Right half-plane pole missing P
9.13 Third-order system missing
9.14 bodenyq.tex P
9.15 Congestion control using TCP/Reno congctrl-margins.tex
9.16 opamp-routh.tex P
9.17 missing P
9.18 Limitations missing
9.19 Limitations missing
9.20 Delay differential equations delayde.tex P
9.21 Cruise control design cruise-pictrl.tex P

Chapter 10 - PID Control

Num Title Filename Stat Auth Comments
10.1 Ideal PID controllers missing
10.2 missing
10.3 missing P
10.4 Ziegler--Nichols tuning missing P
10.5 Vehicle steering steering-pi.tex P
10.6 Congestion control congctrl-pituning.tex P
10.7 Motor drive dcmotor-pdctrl.tex P
10.8 missing
10.9 Tuning rules missing P
10.10 Windup and anti-windup missing
10.11 Windup protection by conditional integration missing P
10.12 pidmethods.tex P
10.13 pidexmps.tex P
10.14 Compartment model compartment-monotone.tex
10.15 missing P
10.16 pirlocus.tex P
10.17 pvtol-pid.tex P
10.18 Ball and beam missing
10.19 balance-pid.tex P

Chapter 11 - Frequency Domain Synthesis

Num Title Filename Stat Auth Comments
11.1 missing
11.2 missing
11.3 missing P
11.4 missing
11.5 Sensitivity of feedback and feedforward missing
11.6 Equivalence of controllers with two degrees of freedom missing
11.7 Disturbance attenuation missing
11.8 Disturbance reduction through feedback missing P
11.9 missing
11.10 Attenuation of low-frequency sinusoidal disturbances missing P
11.11 missing
11.12 missing P
11.13 missing P
11.14 Phase margin formulas missing
11.15 balance-visual.tex P
11.16 Rear-steered bicycle bicycle-rearsteer.tex P
11.17 missing P
11.18 Rise-time/bandwidth product missing
11.19 missing P
11.20 znlimits.tex
11.21 Pole in the right half-plane and time delay missing P
11.22 Cancellation of unstable process zero missing
11.23 Limitations on achievable phase lag missing P
11.24 missing
11.25 Performance characteristics of second-order systems secord-perf.tex P
11.26 secord-rhpz.tex P
11.27 Integral of complementary sensitivity missing P
11.28 Bode's integral missing P
11.29 Lead compensator for an insect flight control system flylead.tex P
11.30 Control of a magnetic levitation system maglev.tex P
11.31 missing P
11.32 pvtol-gangof4.tex

Chapter 12 - Robust Performance

Num Title Filename Stat Auth Comments
12.1 missing P
12.2 missing P
12.3 Difference in sensitivity functions missing P
12.4 The Riemann sphere missing P
12.5 Stability margins missing
12.6 Bode's ideal loop transfer function missing P
12.7 missing P
12.8 Smith predictor missing
12.9 Ideal delay compensator missing
12.10 Vehicle steering missing
12.11 missing
12.12 AFM nanopositioning system missing
12.13 $H_\infty$ control missing
12.14 missing
12.15 missing P
12.16 Robustness using the Nyquist criterion missing P
12.17 Robustness inequalities missing
12.18 missing
12.19 missing
12.20 Disk drive tracking missing