Difference between revisions of "Solutions"

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({{chlink|Robust Performance}})
 
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This page contains a list of the exercises in the text, including
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{{righttoc}}
supplemental problems.  It is mainly intended for use by people who
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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.  Instructors can also use this page to see what problems have solutions available.
are generating solutions to the exercises.
+
 
 +
'''Note:''': if you are looking for solutions to the exercises, you won't find them here.  Solutions to exercises are available to course instructors by contacting {{PUP}}.
  
 
=== Guide to entries ===
 
=== Guide to entries ===
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* Solution status (st): current status of the solutions.  The following abbreviations are used:
 
* Solution status (st): current status of the solutions.  The following abbreviations are used:
 
** C (complete) - complete solution is available
 
** C (complete) - complete solution is available
** P (partial) - partial or preliminary solution is available
+
** A (available) - solution is available, but not yet verified and/or edited
 +
** P (partial) - partial solution is available (some parts, missing figures/code, etc)
 
** I (in progress) - solution is being written, but is not yet available
 
** I (in progress) - solution is being written, but is not yet available
** U (unavailable) - no solution is currently available
+
** U (unavailable) or blank - no solution is currently available
 
** X (not planned) - no solution is planned
 
** X (not planned) - no solution is planned
 
* Author (au): initials for the author of the solutions
 
* Author (au): initials for the author of the solutions
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# 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.
 
# 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.
  
=== {{ch:Introduction}} ===
+
=== {{chlink|Introduction}} ===
 
{{exercise table begin}}
 
{{exercise table begin}}
{{exitem|di=intro|ex=1.1*|ti=Occular motion|fi=eyemotion|st=C|au=KJA|co=|re=}}
+
{{exitem|di=intro|ex=1.1*|ti=[[Exercise: Vestibulo-occular reflex*|Vestibulo-occular reflex]]|fi=eyemotion|st=C|au=KJA|co=|re=}}
{{exitem|di=intro|ex=1.2*|ti=Feedback examples|fi=fbkexamps|st=C|au=Misc|co=|re=}}
+
{{exitem|di=intro|ex=1.2*|ti=[[Exercise: Everyday examples of feedback systems*|Everyday examples of feedback systems]]|fi=fbkexamps|st=C|au=Misc|co=|re=}}
{{exitem|di=intro|ex=1.3*|ti=Human balance|fi=balance-human|st=U|au=|co=Open|re=}}
+
{{exitem|di=intro|ex=1.3*|ti=[[Exercise: Human balance system*|Human balance system]]|fi=balance-human|st=C|au=CL|co=|re=}}
{{exitem|di=intro|ex=1.4*|ti=Cruise control redesign|fi=cruise-redesign|st=U|au=|co=Open|re=}}
+
{{exitem|di=intro|ex=1.4*|ti=[[Exercise: Exploring the performance of a cruise controller*|Exploring the performance of a cruise controller]]|fi=cruise-redesign|st=C|au=CL|co=|re=}}
 
{{exitem|di=intro|ex=1.5*|ti=Integral action|fi=integral|st=C|au=KJA|co=|re=}}
 
{{exitem|di=intro|ex=1.5*|ti=Integral action|fi=integral|st=C|au=KJA|co=|re=}}
{{exitem|di=intro|ex=1.6*|ti=Popular press articles|fi=nytexamps|st=C|au=|co=|re=RMM}}
+
{{exitem|di=intro|ex=1.6*|ti=Popular press articles|fi=nytexamps|st=C|au= RMM |co=|re=}}
 
{{exitem|di=intro|ex=1.7|ti=Milk supply chain|fi=milksupply|st=P|au=KJA|co=Figure missing|re=}}
 
{{exitem|di=intro|ex=1.7|ti=Milk supply chain|fi=milksupply|st=P|au=KJA|co=Figure missing|re=}}
{{exitem|di=intro|ex=1.8|ti=MATLAB cruise control|fi=cruise-mlintro|st=P|au=Misc|co=Preliminary solution available; could be cleaned up|re=}}
+
{{exitem|di=intro|ex=1.8|ti=[[Exercise: Exploring the performance of a cruise controller*|Exploring the performance of a cruise controller (supplemental)]]|fi=cruise-mlintro|st=A|au=CL|co=Cleaned up preliminary solution with model from 3.1.|re=}}
 
{{exitem|di=intro|ex=1.9|ti=MATLAB ball and beam|fi=ballbeam-mlintro|st=P|au=Misc|co=Preliminary solution available; could be cleaned up|re=}}
 
{{exitem|di=intro|ex=1.9|ti=MATLAB ball and beam|fi=ballbeam-mlintro|st=P|au=Misc|co=Preliminary solution available; could be cleaned up|re=}}
{{exitem|di=intro|ex=1.10|ti=Web search: voltage clamp|fi=voltageclamp|st=U|au=|co=Give short intro plus web links|re=}}
+
{{exitem|di=intro|ex=1.10|ti=Web search: voltage clamp|fi=voltageclamp|st=|au=|co=Give short intro plus web links|re=}}
{{exitem|di=intro|ex=1.11|ti=Web search: haptics and force feedback|fi=haptics|st=U|au=|co=Give short intro plus web links|re=}}
+
{{exitem|di=intro|ex=1.11|ti=Web search: haptics and force feedback|fi=haptics|st=|au=|co=Give short intro plus web links|re=}}
{{exitem|di=intro|ex=1.12|ti=Anti-rollover control|fi=rollover|st=U|au=|co=Give short summary of regulations|re=}}
+
{{exitem|di=intro|ex=1.12|ti=Anti-rollover control|fi=rollover|st=|au=|co=Give short summary of regulations|re=}}
 +
{{exercise table end}}
 +
 
 +
=== {{chlink|System Modeling}} ===
 +
{{exercise table begin}}
 +
{{exitem|di=modeling|ex=2.1*|ti=Chain of integrators form|fi=chainofint|st=C|au=SH|co=|re=}}
 +
{{exitem|di=modeling|ex=2.2*|ti=Inverted pendulum|fi=balance-bal2inv|st=C|au=RMM|co=|re=}}
 +
{{exitem|di=modeling|ex=2.3*|ti=Disrete-time dynamics|fi=discrete-solutions|st=C|au=SH|co=|re=}}
 +
{{exitem|di=modeling|ex=2.4*|ti=Keynesian economics|fi=discrete-keynes|st=C|au=SH|co=|re=}}
 +
{{exitem|di=modeling|ex=2.5*|ti=Least squares system identification|fi=sysid-leastsq|st=C|au=SH|co=|re=}}
 +
{{exitem|di=modeling|ex=2.6*|ti=Normalized oscillator dynamics|fi=oscillator|st=C|au=SH|co=|re=}}
 +
{{exitem|di=modeling|ex=2.7*|ti=Electric generator|fi=powergrid|st=A|au=RMM|co=|re=}}
 +
{{exitem|di=modeling|ex=2.8*|ti=Admission control for a queue|fi=queue-admcontrol|st=A|au=KJA|co=|re=}}
 +
{{exitem|di=modeling|ex=2.9*|ti=Biological switch|fi=biocircuits-switchmod|st=A|au=RMM|co=|re=}}
 +
{{exitem|di=modeling|ex=2.10*|ti=Motor drive|fi=dcmotor-modeling|st=C|au=SH|co=|re=}}
 +
{{exitem|di=modeling|ex=2.11|ti=Uncertainty lemon|fi=lemon|st=P|au=|co=|re=}}
 +
{{exitem|di=modeling|ex=2.12|ti=Frequency response|fi=freqresp|st=|au=|co=|re=}}
 +
{{exitem|di=modeling|ex=2.13|ti=Eye and head motion|fi=occular-blockdiag|st=P|au=|co=|re=}}
 +
{{exitem|di=modeling|ex=2.14|ti=Second-order system identification|fi=sysid-logdec|st=|au=|co=|re=}}
 +
{{exitem|di=modeling|ex=2.15|ti=Insect vision|fi=flyvision|st=P|au=|co=|re=}}
 +
{{exitem|di=modeling|ex=2.16|ti=State space model for balance systems|fi=balance-statespace|st=|au=|co=|re=}}
 +
{{exitem|di=modeling|ex=2.17|ti=|fi=fingerflame|st=P|au=|co=|re=}}
 +
{{exitem|di=modeling|ex=2.18|ti=Consensus and invariants|fi=compsys-invariants|st=P|au=|co=|re=}}
 +
{{exitem|di=modeling|ex=2.19|ti=Electric motor|fi=electricmotor|st=P|au=|co=|re=}}
 +
{{exitem|di=modeling|ex=2.20|ti=|fi=exothermic|st=|au=|co=|re=}}
 +
{{exitem|di=modeling|ex=2.21|ti=|fi=caffeine|st=P|au=|co=|re=}}
 +
{{exitem|di=modeling|ex=2.22|ti=|fi=ballbeam-modeling|st=P|au=|co=|re=}}
 +
{{exitem|di=modeling|ex=2.23|ti=|fi=pvtol2invpend|st=|au=|co=|re=}}
 +
{{exitem|di=modeling|ex=2.24|ti=|fi=flyflight|st=|au=|co=|re=}}
 +
{{exitem|di=modeling|ex=2.25|ti=|fi=pendulum|st=P|au=|co=|re=}}
 +
{{exercise table end}}
 +
 
 +
=== {{chlink|Examples}} ===
 +
{{exercise table begin}}
 +
{{exitem|di=examples|ex=3.1*|ti=Cruise control|fi=cruise-hillsim|st=A|au=CL|re=|co=check figures}}
 +
{{exitem|di=examples|ex=3.2*|ti=Bicycle dynamics|fi=bicycle-statespace|st=C|au=RMM|co=|re}}
 +
{{exitem|di=examples|ex=3.3*|ti=Bicycle steering|fi=bicycle-steering|st=C|au=RMM|co=|re=}}
 +
{{exitem|di=examples|ex=3.4*|ti=Operational amplifier circuit|fi=opamp-twopole|st=A|au=SH|co=|re=}}
 +
{{exitem|di=examples|ex=3.5*|ti=Operational amplifier oscillator|fi=opamp-osc|st=A|au=SH|co=|re=}}
 +
{{exitem|di=examples|ex=3.6*|ti=Congestion control using RED~\cite{Low+02:infocom}|fi=congctrl-red|st=P|au=|re=|co=solution consists of reference to research paper}}
 +
{{exitem|di=examples|ex=3.7*|ti=Atomic force microscope with piezo tube|fi=afm-preload|st=A|au=SH|co=|re=}}
 +
{{exitem|di=examples|ex=3.8*|ti=Drug administration|fi=drugadmin-alcohol|st=C|au=|co=|re=}}
 +
{{exitem|di=examples|ex=3.9*|ti=Population dynamics|fi=logistic|st=A|au=SH|co=|re=}}
 +
{{exitem|di=examples|ex=3.10*|ti=Fisheries management|fi=fishery-modeling|st=A|au=|co=|re=}}
 +
{{exitem|di=examples|ex=3.11|ti=Cruise control with powertrain dynamics|fi=powertrain|st=P|au=|co=|re=}}
 +
{{exercise table end}}
 +
 
 +
=== {{chlink|Dynamic Behavior}} ===
 +
{{exercise table begin}}
 +
{{exitem|di=dynamics|ex=4.1*|ti=Time-invariant systems|fi=timeshift|st=A|au=SH|co=|re=}}
 +
{{exitem|di=dynamics|ex=4.2*|ti=Flow in a tank|fi=tank-modeling|st=A|au=SH|co=|re=}}
 +
{{exitem|di=dynamics|ex=4.3*|ti=Cruise control|fi=cruise-phaseplot|st=A|au=CL|co=Solution updated to match dynamics in text|re=}}
 +
{{exitem|di=dynamics|ex=4.4*|ti=Lyapunov functions|fi=lyap-secord|st=A|au=SH|co=V_2(x) has been modified|re=}}
 +
{{exitem|di=dynamics|ex=4.5*|ti=Damped spring--mass system|fi=lyap-oscillator|st=C|au=|co=|re=}}
 +
{{exitem|di=dynamics|ex=4.6*|ti=Electric generator|fi=powergrid|st=A|au=|co=|re=}}
 +
{{exitem|di=dynamics|ex=4.7*|ti=Lyapunov equation|fi=lyapqen|st=A|au=|co=|re=}}
 +
{{exitem|di=dynamics|ex=4.8*|ti=Congestion control|fi=congctrl-lyapstab|st=A|au=|co=|re=}}
 +
{{exitem|di=dynamics|ex=4.9*|ti=Swinging up a pendulum|fi=invpend-swingup|st=A|au=|co=|re=}}
 +
{{exitem|di=dynamics|ex=4.10*|ti=Root locus diagram|fi=rootlocus|st=A|au=|co=|re=}}
 +
{{exitem|di=dynamics|ex=4.11*|ti=Discrete-time Lyapunov function|fi=discrete-lyapunov|st=P|au=|co=Sketch only|re=}}
 +
{{exitem|di=dynamics|ex=4.12*|ti=Operational amplifier oscillator|fi=opamp-oscnl|st=A|au=SH|co=|re=}}
 +
{{exitem|di=dynamics|ex=4.13*|ti=Self-activating genetic circuit|fi=biocircuits-posfbk|st=A|au=|co=|re=}}
 +
{{exitem|di=dynamics|ex=4.14*|ti=Diagonal systems|fi=modal-form|st=P|au=|co=Solution doesn't contain same parts as problem|re=}}
 +
{{exitem|di=dynamics|ex=4.15*|ti=Furuta pendulum|fi=furuta|st=A|au=|co=|re=}}
 +
{{exitem|di=dynamics|ex=4.16*|ti=Routh-Hurwitz criterion|fi=routh|st=A|au=|co=|re=}}
 +
{{exitem|di=dynamics|ex=4.17|ti=Exponential stability|fi=expstab|st=|au=|co=|re=}}
 +
{{exitem|di=dynamics|ex=4.18|ti=Population dynamics|fi=popdyn-logistic|st=P|au=|co=|re=}}
 +
{{exitem|di=dynamics|ex=4.19|ti=Predator prey|fi=predprey-limit|st=P|au=|co=|re=}}
 +
{{exitem|di=dynamics|ex=4.20|ti=Windup protection by conditional integration|fi=windup-condit|st=P|au=|co=|re=}}
 +
{{exitem|di=dynamics|ex=4.21|ti=Gain scheduling, stability|fi=gainsched-stabiility|st=|au=|co=|re=}}
 +
{{exitem|di=dynamics|ex=4.22|ti=Spike generation in neurons|fi=fitzhugh-nagumo|st=P|au=|co=|re=}}
 +
{{exitem|di=dynamics|ex=4.23|ti=Consensus dynamics|fi=compsys-consensus|st=|au=|co=|re=}}
 +
{{exitem|di=dynamics|ex=4.24|ti=Steering dynamics of a ship|fi=tanker-dynamics|st=P|au=|co=|re=}}
 +
{{exitem|di=dynamics|ex=4.25|ti=Pitchfork bifurcation|fi=pitchfork|st=|au=|co=|re=}}
 +
{{exitem|di=dynamics|ex=4.26|ti=Stability examples|fi=stabexmp|st=P|au=|co=|re=}}
 +
{{exitem|di=dynamics|ex=4.27|ti=Lyapunov stability for cruise control|fi=cruise-lyapunov|st=A|au=CL|co=Please add original author of solution to tex file|re=}}
 +
{{exitem|di=dynamics|ex=4.28|ti=Lyapunov stability examples|fi=lyapexmp|st=P|au=|co=|re=}}
 +
{{exercise table end}}
 +
 
 +
=== {{chlink|Linear Systems}} ===
 +
{{exercise table begin}}
 +
{{exitem|di=linsys|ex=5.1*|ti=Response to the derivative of a signal|fi=dersys|st=A|au=SH|co=|re=}}
 +
{{exitem|di=linsys|ex=5.2*|ti=Impulse response and convolution|fi=impulse-response|st=A|au=SH|co=|re=}}
 +
{{exitem|di=linsys|ex=5.3*|ti=Pulse response for a compartment model|fi=compartment-pulse|st=A|au=SH|co=|re=}}
 +
{{exitem|di=linsys|ex=5.4*|ti=Matrix exponential for second-order system|fi=matrixexp|st=P|au=|co=|re=}}
 +
{{exitem|di=linsys|ex=5.5*|ti=Lyapunov function for a linear system|fi=lyap-linear|st=A|au=SH|co=|re=}}
 +
{{exitem|di=linsys|ex=5.6*|ti=Nondiagonal Jordan form|fi=jordan-nontrivial|st=A|au=|co=|re=}}
 +
{{exitem|di=linsys|ex=5.7*|ti=Rise time for a first-order system|fi=risetime-firstord|st=A|au=SH|co=|re=}}
 +
{{exitem|di=linsys|ex=5.8*|ti=Discrete-time systems|fi=discrete-linsys|st=A|au=|co=|re=}}
 +
{{exitem|di=linsys|ex=5.9*|ti=Keynesian economics|fi=discrete-keynes|st=A|au=SH|co=|re=}}
 +
{{exitem|di=linsys|ex=5.10*|ti=|fi=linearization-scalar|st=A|au=|co=|re=}}
 +
{{exitem|di=linsys|ex=5.11*|ti=Transcriptional regulation|fi=biocircuits-negfbk|st=A|au=|co=|re=}}
 +
{{exitem|di=linsys|ex=5.12|ti=Normalized coordinates for second-order system|fi=transform-oscillator|st=|au=|co=|re=}}
 +
{{exitem|di=linsys|ex=5.13|ti=Matrix exponential for Jordan form|fi=matexp-jordan3x3|st=|au=|co=|re=}}
 +
{{exitem|di=linsys|ex=5.14|ti=Solution of a second-order system|fi=conveq-secord|st=|au=|co=|re=}}
 +
{{exitem|di=linsys|ex=5.15|ti=Monotone step response|fi=conveq-monotone|st=|au=|co=|re=}}
 +
{{exitem|di=linsys|ex=5.16|ti=|fi=purecosine|st=P|au=|co=|re=}}
 +
{{exitem|di=linsys|ex=5.17|ti=|fi=linsys-diffeq|st=P|au=|co=|re=}}
 +
{{exitem|di=linsys|ex=5.18|ti=|fi=linexmp-coupled|st=P|au=|co=|re=}}
 +
{{exitem|di=linsys|ex=5.19|ti=State variables in compartment models|fi=compartment-states|st=|au=|co=|re=}}
 +
{{exitem|di=linsys|ex=5.20|ti=|fi=queue-linsys|st=P|au=|co=|re=}}
 +
{{exitem|di=linsys|ex=5.21|ti=Keynes model in continuous time|fi=keynes-ode|st=|au=|co=|re=}}
 +
{{exitem|di=linsys|ex=5.22|ti=|fi=cartpend|st=P|au=|co=|re=}}
 +
{{exitem|di=linsys|ex=5.23|ti=|fi=linsys-sinresp|st=P|au=|co=|re=}}
 +
{{exercise table end}}
 +
 
 +
=== {{chlink|State Feedback}} ===
 +
{{exercise table begin}}
 +
{{exitem|di=statefbk|ex=6.1*|ti=Double integrator|fi=reachable-doubleint|st=A|au=SH|co=|re=}}
 +
{{exitem|di=statefbk|ex=6.2*|ti=Reachability from nonzero initial state|fi=reachable-nonzeroic|st=A|au=SH|co=|re=}}
 +
{{exitem|di=statefbk|ex=6.3*|ti=Unreachable systems|fi=unreachable|st=A|au=SH|co=|re=}}
 +
{{exitem|di=statefbk|ex=6.4*|ti=Integral feedback for rejecting constant disturbances|fi=integral-noiserej|st=A|au=|co=|re=}}
 +
{{exitem|di=statefbk|ex=6.5*|ti=Rear-steered bicycle|fi=bicycle-rearsteer|st=A|au=|co=|re=}}
 +
{{exitem|di=statefbk|ex=6.6*|ti=Characteristic polynomial for reachable canonical form|fi=reachable-form|st=A|au=SH|co=|re=}}
 +
{{exitem|di=statefbk|ex=6.7*|ti=Reachability matrix for reachable canonical form|fi=inverse-reachmat|st=A|au=SH|co=|re=}}
 +
{{exitem|di=statefbk|ex=6.8*|ti=Non-maintainable equilibria|fi=pendcart-noref|st=A|au=SH|co=|re=}}
 +
{{exitem|di=statefbk|ex=6.9*|ti=Eigenvalue assignment for unreachable system|fi=unreachable-assign|st=A|au=SH|co=|re=}}
 +
{{exitem|di=statefbk|ex=6.10*|ti=Cayley--Hamilton theorem|fi=cayley-hamilton|st=A|au=|co=|re=}}
 +
{{exitem|di=statefbk|ex=6.11*|ti=Motor drive|fi=dcmotor-statefbk|st=A|au=|co=|re=}}
 +
{{exitem|di=statefbk|ex=6.12*|ti=Whipple bicycle model|fi=bicycle-whipple|st=A|au=|co=|re=}}
 +
{{exitem|di=statefbk|ex=6.13*|ti=Atomic force microscope|fi=afm-scalelqr|st=A|au=|co=|re=}}
 +
{{exitem|di=statefbk|ex=6.14*|ti=Step response for a second order system|fi=secord-zero|st=A|au=|co=|re=}}
 +
{{exitem|di=statefbk|ex=6.15*|ti=Bryson's rule|fi=brysons-rule|st=C|au=|co=|re=}}
 +
{{exitem|di=statefbk|ex=6.16|ti=|fi=integral-refgain|st=|au=|co=|re=}}
 +
{{exitem|di=statefbk|ex=6.17|ti=Unreachable compartment model|fi=compartment-nonreach.pst|st=P|au=|co=|re=}}
 +
{{exitem|di=statefbk|ex=6.18|ti=|fi=refgain-direct|st=|au=|co=|re=}}
 +
{{exitem|di=statefbk|ex=6.19|ti=|fi=cruise-norefgain|st=|au=|co=|re=}}
 +
{{exercise table end}}
 +
 
 +
=== {{chlink|Output Feedback}} ===
 +
{{exercise table begin}}
 +
{{exitem|di=outputfbk|ex=7.1*|ti=Coordinate transformations|fi=coordxform|st=A|au=SH|co=|re=}}
 +
{{exitem|di=outputfbk|ex=7.2*|ti=|fi=unobservable|st=A|au=SH|co=|re=}}
 +
{{exitem|di=outputfbk|ex=7.3*|ti=Observable canonical form|fi=obsform-transform|st=A|au=SH|co=|re=}}
 +
{{exitem|di=outputfbk|ex=7.4*|ti=Bicycle dynamics|fi=bicycle-observability|st=A|au=|co=|re=}}
 +
{{exitem|di=outputfbk|ex=7.5*|ti=Integral action|fi=integral-action|st=A|au=|co=|re=}}
 +
{{exitem|di=outputfbk|ex=7.6*|ti=Vectored thrust aircraft|fi=pvtol-ssctrl|st=A|au=|co=|re=}}
 +
{{exitem|di=outputfbk|ex=7.7*|ti=Uniqueness of observers|fi=observer-assign|st=A|au=|co=|re=}}
 +
{{exitem|di=outputfbk|ex=7.8*|ti=Observers using differentiation|fi=diff|st=A|au=SH|co=|re=}}
 +
{{exitem|di=outputfbk|ex=7.9*|ti=Observer for Teorell's compartment model|fi=compartment-teorellobs|st=A|au=|co=|re=}}
 +
{{exitem|di=outputfbk|ex=7.10*|ti=Observer design for motor drive|fi=dcmotor-observer|st=A|au=|co=|re=}}
 +
{{exitem|di=outputfbk|ex=7.11*|ti=Feedforward design for motor drive|fi=dcmotor-feedforward|st=A|au=|co=|re=}}
 +
{{exitem|di=outputfbk|ex=7.12*|ti=Whipple bicycle model|fi=bicycle-whipple|st=A|au=|co=|re=}}
 +
{{exitem|di=outputfbk|ex=7.13*|ti=Discrete-time random walk|fi=kalman-randomwalk|st=A|au=|co=|re=}}
 +
{{exitem|di=outputfbk|ex=7.14*|ti=Kalman decomposition|fi=kalman-decomp-2x2|st=A|au=SH|co=|re=}}
 +
{{exitem|di=outputfbk|ex=7.15|ti=|fi=secord-observer|st=P|au=|co=|re=}}
 +
{{exitem|di=outputfbk|ex=7.16|ti=Balance system|fi=balance-observable|st=|au=|co=|re=}}
 +
{{exitem|di=outputfbk|ex=7.17|ti=Balance system with biased measurement|fi=balance-statectrl|st=|au=|co=|re=}}
 +
{{exitem|di=outputfbk|ex=7.18|ti=Duality|fi=observer-duality|st=|au=|co=|re=}}
 +
{{exitem|di=outputfbk|ex=7.19|ti=Balance system|fi=cartpend-observer|st=|au=|co=|re=}}
 +
{{exitem|di=outputfbk|ex=7.20|ti=Trajectory generation|fi=trajgen-scalar|st=|au=|co=|re=}}
 +
{{exitem|di=outputfbk|ex=7.21|ti=Selection of eigenvalues|fi=compartment-poleplace|st=|au=|co=|re=}}
 +
{{exitem|di=outputfbk|ex=7.22|ti=Kalman filter for scalar ODE|fi=kalman-scalar|st=P|au=|co=|re=}}
 +
{{exercise table end}}
 +
 
 +
=== {{chlink|Transfer Functions}} ===
 +
{{exercise table begin}}
 +
{{exitem|di=xferfcns|ex=8.1*|ti=Steady state response to a sinusoid|fi=sininput|st=A|au=SH|co=}}
 +
{{exitem|di=xferfcns|ex=8.2*|ti=Modal response for a first order system|fi=modalinput|st=A|au=SH|co=|re=}}
 +
{{exitem|di=xferfcns|ex=8.3*|ti=Inverted pendulum|fi=invpend-xferfcn|st=A|au=SH|co=|re=}}
 +
{{exitem|di=xferfcns|ex=8.4*|ti=Solutions corresponding to poles and zeros|fi=pzsolns|st=A|au=SH|co=|re=}}
 +
{{exitem|di=xferfcns|ex=8.5*|ti=Operational amplifier|fi=opamp-pictrl|st=A|au=SH|co=|re=}}
 +
{{exitem|di=xferfcns|ex=8.6*|ti=Transfer function for state space system|fi=ssxferfcn|st=A|au=SH|co=|re=}}
 +
{{exitem|di=xferfcns|ex=8.7*|ti=Kalman decomposition|fi=kalmandecomp|st=A|au=|co=|re=}}
 +
{{exitem|di=xferfcns|ex=8.8*|ti=Transfer functions for control systems|fi=ctrlxferfcns|st=A|au=SH|co=|re=}}
 +
{{exitem|di=xferfcns|ex=8.9*|ti=Bode plot for a simple zero|fi=bode-zero|st=A|au=SH|co=|re=}}
 +
{{exitem|di=xferfcns|ex=8.10*|ti=Vectored thrust aircraft|fi=pvtol-lateraltf|st=A|au=SH|co=|re=}}
 +
{{exitem|di=xferfcns|ex=8.11*|ti=Common poles|fi=missing|st=A|au=|co=|re=}}
 +
{{exitem|di=xferfcns|ex=8.12*|ti=Congestion control|fi=congctrl-xferfcns|st=P|au=|co=|re=}}
 +
{{exitem|di=xferfcns|ex=8.13*|ti=Inverted pendulum with PD control|fi=invpend-pzcancel|st=A|au=SH|co=|re=}}
 +
{{exitem|di=xferfcns|ex=8.14*|ti=Vehicle suspension|fi=vehicle-quartercar|st=A|au=SH|co=|re=}}
 +
{{exitem|di=xferfcns|ex=8.15*|ti=Vibration absorber|fi=vibdamper|st=A|au=SH|co=|re=}}
 +
{{exitem|di=xferfcns|ex=8.16|ti=|fi=freqexamps|st=P|au=|co=|re=}}
 +
{{exitem|di=xferfcns|ex=8.17|ti=|fi=model-simplification|st=|au=|co=|re=}}
 +
{{exitem|di=xferfcns|ex=8.18|ti=|fi=cruise-pictrl|st=P|au=|co=|re=}}
 +
{{exitem|di=xferfcns|ex=8.19|ti=|fi=dcmotor-xferfcn|st=|au=|co=|re=}}
 +
{{exitem|di=xferfcns|ex=8.20|ti=|fi=xferfcn-match|st=|au=|co=|re=}}
 +
{{exitem|di=xferfcns|ex=8.21|ti=|fi=heat-propogation|st=P|au=|co=|re=}}
 +
{{exitem|di=xferfcns|ex=8.22|ti=|fi=queue-xferfcn|st=P|au=|co=|re=}}
 +
{{exitem|di=xferfcns|ex=8.23|ti=|fi=lq-scalar|st=|au=|co=|re=}}
 +
{{exercise table end}}
 +
 
 +
=== {{chlink|Frequency Domain Analysis}} ===
 +
{{exercise table begin}}
 +
{{exitem|di=loopanal|ex=9.1*|ti=Operational amplifier|fi=opamp-unitygain|st=A|au=|co=|re=}}
 +
{{exitem|di=loopanal|ex=9.2*|ti=Atomic force microscope|fi=afm-tapping|st=A|au=|co=|re=}}
 +
{{exitem|di=loopanal|ex=9.3*|ti=Heat conduction|fi=heatcond-nyquist|st=P|au=|co=|re=}}
 +
{{exitem|di=loopanal|ex=9.4*|ti=Vectored thrust aircraft|fi=pvtol-looptf|st=A|au=|co=|re=}}
 +
{{exitem|di=loopanal|ex=9.5*|ti=Vehicle steering|fi=steering-margins|st=A|au=|co=|re=}}
 +
{{exitem|di=loopanal|ex=9.6*|ti=Stability margins for second-order systems|fi=secord-margins|st=A|au=|co=|re=}}
 +
{{exitem|di=loopanal|ex=9.7*|ti=Congestion control in overload conditions|fi=congctrl-overload|st=A|au=|co=|re=}}
 +
{{exitem|di=loopanal|ex=9.8*|ti=Bode's formula|fi=bode-weight|st=A|au=|co=|re=}}
 +
{{exitem|di=loopanal|ex=9.9*|ti=Pad\'e approximation to a time delay|fi=pade-approx|st=A|au=SH|co='a' is not defined|re=}}
 +
{{exitem|di=loopanal|ex=9.10*|ti=Inverse response|fi=inverse-response|st=A|au=|co=|re=}}
 +
{{exitem|di=loopanal|ex=9.11*|ti=Describing function analysis|fi=descfcn-hystrelay|st=A|au=SH|co=|re=}}
 +
{{exitem|di=loopanal|ex=9.12|ti=Right half-plane pole|fi=nyquist-rhp|st=P|au=|co=|re=}}
 +
{{exitem|di=loopanal|ex=9.13|ti=Third-order system|fi=nyquist-thirdorder|st=|au=|co=|re=}}
 +
{{exitem|di=loopanal|ex=9.14|ti=|fi=bodenyq|st=P|au=|co=|re=}}
 +
{{exitem|di=loopanal|ex=9.15|ti=Congestion control using TCP/Reno|fi=congctrl-margins|st=|au=|co=|re=}}
 +
{{exitem|di=loopanal|ex=9.16|ti=|fi=opamp-routh|st=P|au=|co=|re=}}
 +
{{exitem|di=loopanal|ex=9.17|ti=|fi=cruise-nyquist-alt|st=P|au=|co=|re=}}
 +
{{exitem|di=loopanal|ex=9.18|ti=Limitations|fi=invpend-limits|st=|au=|co=|re=}}
 +
{{exitem|di=loopanal|ex=9.19|ti=Limitations|fi=invpend-delay|st=|au=|co=|re=}}
 +
{{exitem|di=loopanal|ex=9.20|ti=Delay differential equations|fi=delayde|st=P|au=|co=|re=}}
 +
{{exitem|di=loopanal|ex=9.21|ti=Cruise control design|fi=cruise-pictrl|st=P|au=CL|co=Model may need updating; check for duplication with similar exercise in previous chapter|re=}}
 +
{{exercise table end}}
 +
 
 +
=== {{chlink|PID Control}} ===
 +
{{exercise table begin}}
 +
{{exitem|di=pid|ex=10.1*|ti=Ideal PID controllers|fi=pid-ideal|st=A|au=SH|co=|re=}}
 +
{{exitem|di=pid|ex=10.2*|ti=PI for second order process|fi=secord-pid|st=A|au=SH|co=|re=}}
 +
{{exitem|di=pid|ex=10.3*|ti=Integral control for two pole system|fi=integral-twopole|st=A|au=|co=|re=}}
 +
{{exitem|di=pid|ex=10.4*|ti=Ziegler-Nichols tuning|fi=zntuning-delint|st=A|au=|co=|re=}}
 +
{{exitem|di=pid|ex=10.5*|ti=Vehicle steering|fi=steering-pi|st=A|au=|co=|re=}}
 +
{{exitem|di=pid|ex=10.6*|ti=Congestion control|fi=congctrl-pituning|st=A|au=|co=|re=}}
 +
{{exitem|di=pid|ex=10.7*|ti=Motor drive|fi=dcmotor-pdctrl|st=A|au=|co=|re=}}
 +
{{exitem|di=pid|ex=10.8*|ti=Motor drive with first order filter|fi=derfilter|st=A|au=|co=|re=}}
 +
{{exitem|di=pid|ex=10.9*|ti=Tuning rules|fi=zntuning-examples|st=A|au=|co=|re=}}
 +
{{exitem|di=pid|ex=10.10*|ti=Windup and anti-windup|fi=antiwindup-intpi|st=A|au=SH|co=|re=}}
 +
{{exitem|di=pid|ex=10.11*|ti=Windup protection by conditional integration|fi=antiwindup-condint|st=A|au=|co=|re=}}
 +
{{exitem|di=pid|ex=10.12|ti=|fi=pidmethods|st=P|au=|co=|re=}}
 +
{{exitem|di=pid|ex=10.13|ti=|fi=pidexmps|st=P|au=|co=|re=}}
 +
{{exitem|di=pid|ex=10.14|ti=Compartment model|fi=compartment-monotone|st=|au=|co=|re=}}
 +
{{exitem|di=pid|ex=10.15|ti=|fi=plasma-oven|st=P|au=|co=|re=}}
 +
{{exitem|di=pid|ex=10.16|ti=|fi=pirlocus|st=P|au=|co=|re=}}
 +
{{exitem|di=pid|ex=10.17|ti=|fi=pvtol-pid|st=P|au=|co=|re=}}
 +
{{exitem|di=pid|ex=10.18|ti=Ball and beam|fi=ballbeam-pid|st=|au=|co=|re=}}
 +
{{exitem|di=pid|ex=10.19|ti=|fi=balance-pid|st=P|au=|co=|re=}}
 +
{{exercise table end}}
 +
 
 +
=== {{chlink|Frequency Domain Synthesis}} ===
 +
{{exercise table begin}}
 +
{{exitem|di=loopsyn|ex=11.1*|ti=Gang of Four transfer functions|fi=gangoffour|st=A|au=|co=|re=}}
 +
{{exitem|di=loopsyn|ex=11.2*|ti=Gang of Four for system with RHP pole, proportional control|fi=rhppole-cancel|st=A|au=|co=Missing figures|re=}}
 +
{{exitem|di=loopsyn|ex=11.3*|ti=Gang of Four for H infinity structure|fi=gangoffour-hinfstruc|st=A|au=|co=|re=}}
 +
{{exitem|di=loopsyn|ex=11.4*|ti=Feedforward compensator for spring-mass system|fi=springmass-feedforward|st=A|au=|co=|re=}}
 +
{{exitem|di=loopsyn|ex=11.5*|ti=Sensitivity of feedback and feedforward|fi=sensitivity-gyr|st=A|au=|co=|re=}}
 +
{{exitem|di=loopsyn|ex=11.6*|ti=Equivalence of controllers with two degrees of freedom|fi=twodof-equiv|st=A|au=|co=|re=}}
 +
{{exitem|di=loopsyn|ex=11.7*|ti=Disturbance attenuation|fi=sensitivity-atten|st=A|au=|co=|re=}}
 +
{{exitem|di=loopsyn|ex=11.8*|ti=Disturbance reduction through feedback|fi=sensitivity-twopole|st=A|au=|co=|re=}}
 +
{{exitem|di=loopsyn|ex=11.9*|ti=High frequency measurement noise approximation|fi=noiseapprox|st=A|au=|co=|re=}}
 +
{{exitem|di=loopsyn|ex=11.10*|ti=Attenuation of low-frequency sinusoidal disturbances|fi=sinusoid-atten|st=A|au=|co=|re=}}
 +
{{exitem|di=loopsyn|ex=11.11*|ti=Lead compensation|fi=lead-phasecalc|st=A|au=|co=|re=}}
 +
{{exitem|di=loopsyn|ex=11.12*|ti=RHP pole/zero pair|fi=rhppzpair|st=A|au=|co=|re=}}
 +
{{exitem|di=loopsyn|ex=11.13*|ti=Sensitivity bounds for RHP pole/zero pair|fi=sensitivity-pzdel|st=A|au=|co=|re=}}
 +
{{exitem|di=loopsyn|ex=11.14*|ti=Phase margin formulas|fi=sensitivity-pm|st=A|au=|co=|re=}}
 +
{{exitem|di=loopsyn|ex=11.15*|ti=Stabilization of an inverted pendulum with visual feedback|fi=balance-visual|st=A|au=|co=|re=}}
 +
{{exitem|di=loopsyn|ex=11.16*|ti=Rear-steered bicycle|fi=bicycle-rearsteer|st=A|au=|co=|re=}}
 +
{{exitem|di=loopsyn|ex=11.17*|ti=|fi=bode-compsens|st=A|au=|co=|re=}}
 +
{{exitem|di=loopsyn|ex=11.18|ti=Rise-time/bandwidth product|fi=risetime-bandwidth|st=P|au=|co=|re=}}
 +
{{exitem|di=loopsyn|ex=11.19|ti=|fi=laplace-smalltime|st=P|au=|co=|re=}}
 +
{{exitem|di=loopsyn|ex=11.20|ti=|fi=znlimits|st=P|au=|co=|re=}}
 +
{{exitem|di=loopsyn|ex=11.21|ti=Pole in the right half-plane and time delay|fi=rhppole-delay|st=P|au=|co=|re=}}
 +
{{exitem|di=loopsyn|ex=11.22|ti=Cancellation of unstable process zero|fi=steering-reverse|st=|au=|co=|re=}}
 +
{{exitem|di=loopsyn|ex=11.23|ti=Limitations on achievable phase lag|fi=rhppole-limitations|st=P|au=|co=|re=}}
 +
{{exitem|di=loopsyn|ex=11.24|ti=|fi=pvtol-gangoffour|st=|au=|co=|re=}}
 +
{{exitem|di=loopsyn|ex=11.25|ti=Performance characteristics of second-order systems|fi=secord-perf|st=P|au=|co=|re=}}
 +
{{exitem|di=loopsyn|ex=11.26|ti=|fi=secord-rhpz|st=P|au=|co=|re=}}
 +
{{exitem|di=loopsyn|ex=11.27|ti=Integral of complementary sensitivity|fi=bode-compsens-alt|st=P|au=|co=|re=}}
 +
{{exitem|di=loopsyn|ex=11.28|ti=Bode's integral|fi=bode-compsens-norolloff|st=P|au=|co=|re=}}
 +
{{exitem|di=loopsyn|ex=11.29|ti=Lead compensator for an insect flight control system|fi=flylead|st=P|au=|co=|re=}}
 +
{{exitem|di=loopsyn|ex=11.30|ti=Control of a magnetic levitation system|fi=maglev|st=P|au=|co=|re=}}
 +
{{exitem|di=loopsyn|ex=11.31|ti=|fi=pvtol-gangof4|st=|au=|co=|re=}}
 +
{{exitem|di=loopsyn|ex=11.32|ti=Relationship between gain and sensitivity crossover frequencies|fi=sensitivity-margins|st=P|au=KJA|co=|re=}}
 +
{{exercise table end}}
 +
 
 +
=== {{chlink|Robust Performance}} ===
 +
{{exercise table begin}}
 +
{{exitem|di= robperf |ex=12.1*|ti=Uncertainty between two first-order systems|fi=uncertainty-onepole|st=A|au=|co=|re=}}
 +
{{exitem|di= robperf |ex=12.2*|ti=Uncertainty between two second-order systems|fi=uncertainty-twopole|st=A|au=|co=|re=}}
 +
{{exitem|di= robperf |ex=12.3*|ti=Difference in sensitivity functions|fi=sensitivity-difference|st=A|au=|co=|re=}}
 +
{{exitem|di= robperf |ex=12.4*|ti=The Riemann sphere|fi=vinnecombe-sphere|st=A|au=|co=|re=}}
 +
{{exitem|di= robperf |ex=12.5*|ti=Stability margins|fi=sensitivity-maxpm|st=A|au=|co=|re=}}
 +
{{exitem|di= robperf |ex=12.6|*ti=Bode's ideal loop transfer function|fi=idealbode-margins|st=A|au=|co=|re=}}
 +
{{exitem|di= robperf |ex=12.7*|ti=Fractional loop transfer function|fi=idealbode-fracsys|st=A|au=|co=|re=}}
 +
{{exitem|di= robperf |ex=12.8*|ti=Smith predictor|fi=smith-predictor|st=A|au=|co=|re=}}
 +
{{exitem|di= robperf |ex=12.9*|ti=Ideal delay compensator|fi=delay-compensation|st=A|au=|co=|re=}}
 +
{{exitem|di= robperf |ex=12.10*|ti=Vehicle steering|fi=steering-nyquist|st=A|au=|co=|re=}}
 +
{{exitem|di= robperf |ex=12.11*|ti=Design with dominant pole specification|fi=design-fourthord|st=A|au=|co=|re=}}
 +
{{exitem|di= robperf |ex=12.12*|ti=AFM nanopositioning system|fi=afm-robustpid|st=A|au=|co=|re=}}
 +
{{exitem|di= robperf |ex=12.13*|ti=$H_\infty$ control|fi=hinf-singval|st=A|au=|co=|re=}}
 +
{{exitem|di= robperf |ex=12.14*|ti=Vinnicombe metric computation|fi=hinf-vinnecombe|st=A|au=|co=Solution consists of a citation|re=}}
 +
{{exitem|di= robperf |ex=12.15*|ti=Robustness of an observer-based design|fi=robust-statespace|st=A|au=|co=Solution is very long|re=}}
 +
{{exitem|di= robperf |ex=12.16*|ti=Robustness using the Nyquist criterion|fi=robust-nyquist|st=P|au=|co=Missing figures|re=}}
 +
{{exitem|di= robperf |ex=12.17|ti=Robustness inequalities|fi=robustness-conditions|st=|au=|co=|re=}}
 +
{{exitem|di= robperf |ex=12.18|ti=|fi=vinnecombe-nonunity|st=|au=|co=|re=}}
 +
{{exitem|di= robperf |ex=12.19|ti=|fi=vinnecombe-onepole|st=|au=|co=|re=}}
 +
{{exitem|di=robperf|ex=12.20|ti=Disk drive tracking|fi=missing|st=|au=|co=|re=}}
 
{{exercise table end}}
 
{{exercise table end}}

Latest revision as of 13:24, 19 August 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. Instructors can also use this page to see what problems have solutions available.

Note:: if you are looking for solutions to the exercises, you won't find them here. Solutions to exercises are available to course instructors by contacting Princeton University Press.

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
    • A (available) - solution is available, but not yet verified and/or edited
    • P (partial) - partial solution is available (some parts, missing figures/code, etc)
    • I (in progress) - solution is being written, but is not yet available
    • U (unavailable) or blank - 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* Vestibulo-occular reflex eyemotion C KJA
1.2* Everyday examples of feedback systems fbkexamps C Misc
1.3* Human balance system balance-human C CL
1.4* Exploring the performance of a cruise controller cruise-redesign C CL
1.5* Integral action integral C KJA
1.6* Popular press articles nytexamps C RMM
1.7 Milk supply chain milksupply P KJA Figure missing
1.8 Exploring the performance of a cruise controller (supplemental) cruise-mlintro A CL Cleaned up preliminary solution with model from 3.1.
1.9 MATLAB ball and beam ballbeam-mlintro P Misc Preliminary solution available; could be cleaned up
1.10 Web search: voltage clamp voltageclamp Give short intro plus web links
1.11 Web search: haptics and force feedback haptics Give short intro plus web links
1.12 Anti-rollover control rollover Give short summary of regulations

Chapter 2 - System Modeling

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

Chapter 3 - Examples

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

Chapter 4 - Dynamic Behavior

Num Title Filename Stat Auth Comments
4.1* Time-invariant systems timeshift A SH
4.2* Flow in a tank tank-modeling A SH
4.3* Cruise control cruise-phaseplot A CL Solution updated to match dynamics in text
4.4* Lyapunov functions lyap-secord A SH V_2(x) has been modified
4.5* Damped spring--mass system lyap-oscillator C
4.6* Electric generator powergrid A
4.7* Lyapunov equation lyapqen A
4.8* Congestion control congctrl-lyapstab A
4.9* Swinging up a pendulum invpend-swingup A
4.10* Root locus diagram rootlocus A
4.11* Discrete-time Lyapunov function discrete-lyapunov P Sketch only
4.12* Operational amplifier oscillator opamp-oscnl A SH
4.13* Self-activating genetic circuit biocircuits-posfbk A
4.14* Diagonal systems modal-form P Solution doesn't contain same parts as problem
4.15* Furuta pendulum furuta A
4.16* Routh-Hurwitz criterion routh A
4.17 Exponential stability expstab
4.18 Population dynamics popdyn-logistic P
4.19 Predator prey predprey-limit P
4.20 Windup protection by conditional integration windup-condit P
4.21 Gain scheduling, stability gainsched-stabiility
4.22 Spike generation in neurons fitzhugh-nagumo P
4.23 Consensus dynamics compsys-consensus
4.24 Steering dynamics of a ship tanker-dynamics P
4.25 Pitchfork bifurcation pitchfork
4.26 Stability examples stabexmp P
4.27 Lyapunov stability for cruise control cruise-lyapunov A CL Please add original author of solution to tex file
4.28 Lyapunov stability examples lyapexmp P

Chapter 5 - Linear Systems

Num Title Filename Stat Auth Comments
5.1* Response to the derivative of a signal dersys A SH
5.2* Impulse response and convolution impulse-response A SH
5.3* Pulse response for a compartment model compartment-pulse A SH
5.4* Matrix exponential for second-order system matrixexp P
5.5* Lyapunov function for a linear system lyap-linear A SH
5.6* Nondiagonal Jordan form jordan-nontrivial A
5.7* Rise time for a first-order system risetime-firstord A SH
5.8* Discrete-time systems discrete-linsys A
5.9* Keynesian economics discrete-keynes A SH
5.10* linearization-scalar A
5.11* Transcriptional regulation biocircuits-negfbk A
5.12 Normalized coordinates for second-order system transform-oscillator
5.13 Matrix exponential for Jordan form matexp-jordan3x3
5.14 Solution of a second-order system conveq-secord
5.15 Monotone step response conveq-monotone
5.16 purecosine P
5.17 linsys-diffeq P
5.18 linexmp-coupled P
5.19 State variables in compartment models compartment-states
5.20 queue-linsys P
5.21 Keynes model in continuous time keynes-ode
5.22 cartpend P
5.23 linsys-sinresp P

Chapter 6 - State Feedback

Num Title Filename Stat Auth Comments
6.1* Double integrator reachable-doubleint A SH
6.2* Reachability from nonzero initial state reachable-nonzeroic A SH
6.3* Unreachable systems unreachable A SH
6.4* Integral feedback for rejecting constant disturbances integral-noiserej A
6.5* Rear-steered bicycle bicycle-rearsteer A
6.6* Characteristic polynomial for reachable canonical form reachable-form A SH
6.7* Reachability matrix for reachable canonical form inverse-reachmat A SH
6.8* Non-maintainable equilibria pendcart-noref A SH
6.9* Eigenvalue assignment for unreachable system unreachable-assign A SH
6.10* Cayley--Hamilton theorem cayley-hamilton A
6.11* Motor drive dcmotor-statefbk A
6.12* Whipple bicycle model bicycle-whipple A
6.13* Atomic force microscope afm-scalelqr A
6.14* Step response for a second order system secord-zero A
6.15* Bryson's rule brysons-rule C
6.16 integral-refgain
6.17 Unreachable compartment model compartment-nonreach.pst P
6.18 refgain-direct
6.19 cruise-norefgain

Chapter 7 - Output Feedback

Num Title Filename Stat Auth Comments
7.1* Coordinate transformations coordxform A SH
7.2* unobservable A SH
7.3* Observable canonical form obsform-transform A SH
7.4* Bicycle dynamics bicycle-observability A
7.5* Integral action integral-action A
7.6* Vectored thrust aircraft pvtol-ssctrl A
7.7* Uniqueness of observers observer-assign A
7.8* Observers using differentiation diff A SH
7.9* Observer for Teorell's compartment model compartment-teorellobs A
7.10* Observer design for motor drive dcmotor-observer A
7.11* Feedforward design for motor drive dcmotor-feedforward A
7.12* Whipple bicycle model bicycle-whipple A
7.13* Discrete-time random walk kalman-randomwalk A
7.14* Kalman decomposition kalman-decomp-2x2 A SH
7.15 secord-observer P
7.16 Balance system balance-observable
7.17 Balance system with biased measurement balance-statectrl
7.18 Duality observer-duality
7.19 Balance system cartpend-observer
7.20 Trajectory generation trajgen-scalar
7.21 Selection of eigenvalues compartment-poleplace
7.22 Kalman filter for scalar ODE kalman-scalar P

Chapter 8 - Transfer Functions

Num Title Filename Stat Auth Comments
8.1* Steady state response to a sinusoid sininput A SH
8.2* Modal response for a first order system modalinput A SH
8.3* Inverted pendulum invpend-xferfcn A SH
8.4* Solutions corresponding to poles and zeros pzsolns A SH
8.5* Operational amplifier opamp-pictrl A SH
8.6* Transfer function for state space system ssxferfcn A SH
8.7* Kalman decomposition kalmandecomp A
8.8* Transfer functions for control systems ctrlxferfcns A SH
8.9* Bode plot for a simple zero bode-zero A SH
8.10* Vectored thrust aircraft pvtol-lateraltf A SH
8.11* Common poles missing A
8.12* Congestion control congctrl-xferfcns P
8.13* Inverted pendulum with PD control invpend-pzcancel A SH
8.14* Vehicle suspension vehicle-quartercar A SH
8.15* Vibration absorber vibdamper A SH
8.16 freqexamps P
8.17 model-simplification
8.18 cruise-pictrl P
8.19 dcmotor-xferfcn
8.20 xferfcn-match
8.21 heat-propogation P
8.22 queue-xferfcn P
8.23 lq-scalar

Chapter 9 - Frequency Domain Analysis

Num Title Filename Stat Auth Comments
9.1* Operational amplifier opamp-unitygain A
9.2* Atomic force microscope afm-tapping A
9.3* Heat conduction heatcond-nyquist P
9.4* Vectored thrust aircraft pvtol-looptf A
9.5* Vehicle steering steering-margins A
9.6* Stability margins for second-order systems secord-margins A
9.7* Congestion control in overload conditions congctrl-overload A
9.8* Bode's formula bode-weight A
9.9* Pad\'e approximation to a time delay pade-approx A SH 'a' is not defined
9.10* Inverse response inverse-response A
9.11* Describing function analysis descfcn-hystrelay A SH
9.12 Right half-plane pole nyquist-rhp P
9.13 Third-order system nyquist-thirdorder
9.14 bodenyq P
9.15 Congestion control using TCP/Reno congctrl-margins
9.16 opamp-routh P
9.17 cruise-nyquist-alt P
9.18 Limitations invpend-limits
9.19 Limitations invpend-delay
9.20 Delay differential equations delayde P
9.21 Cruise control design cruise-pictrl P CL Model may need updating; check for duplication with similar exercise in previous chapter

Chapter 10 - PID Control

Num Title Filename Stat Auth Comments
10.1* Ideal PID controllers pid-ideal A SH
10.2* PI for second order process secord-pid A SH
10.3* Integral control for two pole system integral-twopole A
10.4* Ziegler-Nichols tuning zntuning-delint A
10.5* Vehicle steering steering-pi A
10.6* Congestion control congctrl-pituning A
10.7* Motor drive dcmotor-pdctrl A
10.8* Motor drive with first order filter derfilter A
10.9* Tuning rules zntuning-examples A
10.10* Windup and anti-windup antiwindup-intpi A SH
10.11* Windup protection by conditional integration antiwindup-condint A
10.12 pidmethods P
10.13 pidexmps P
10.14 Compartment model compartment-monotone
10.15 plasma-oven P
10.16 pirlocus P
10.17 pvtol-pid P
10.18 Ball and beam ballbeam-pid
10.19 balance-pid P

Chapter 11 - Frequency Domain Synthesis

Num Title Filename Stat Auth Comments
11.1* Gang of Four transfer functions gangoffour A
11.2* Gang of Four for system with RHP pole, proportional control rhppole-cancel A Missing figures
11.3* Gang of Four for H infinity structure gangoffour-hinfstruc A
11.4* Feedforward compensator for spring-mass system springmass-feedforward A
11.5* Sensitivity of feedback and feedforward sensitivity-gyr A
11.6* Equivalence of controllers with two degrees of freedom twodof-equiv A
11.7* Disturbance attenuation sensitivity-atten A
11.8* Disturbance reduction through feedback sensitivity-twopole A
11.9* High frequency measurement noise approximation noiseapprox A
11.10* Attenuation of low-frequency sinusoidal disturbances sinusoid-atten A
11.11* Lead compensation lead-phasecalc A
11.12* RHP pole/zero pair rhppzpair A
11.13* Sensitivity bounds for RHP pole/zero pair sensitivity-pzdel A
11.14* Phase margin formulas sensitivity-pm A
11.15* Stabilization of an inverted pendulum with visual feedback balance-visual A
11.16* Rear-steered bicycle bicycle-rearsteer A
11.17* bode-compsens A
11.18 Rise-time/bandwidth product risetime-bandwidth P
11.19 laplace-smalltime P
11.20 znlimits P
11.21 Pole in the right half-plane and time delay rhppole-delay P
11.22 Cancellation of unstable process zero steering-reverse
11.23 Limitations on achievable phase lag rhppole-limitations P
11.24 pvtol-gangoffour
11.25 Performance characteristics of second-order systems secord-perf P
11.26 secord-rhpz P
11.27 Integral of complementary sensitivity bode-compsens-alt P
11.28 Bode's integral bode-compsens-norolloff P
11.29 Lead compensator for an insect flight control system flylead P
11.30 Control of a magnetic levitation system maglev P
11.31 pvtol-gangof4
11.32 Relationship between gain and sensitivity crossover frequencies sensitivity-margins P KJA

Chapter 12 - Robust Performance

Num Title Filename Stat Auth Comments
12.1* Uncertainty between two first-order systems uncertainty-onepole A
12.2* Uncertainty between two second-order systems uncertainty-twopole A
12.3* Difference in sensitivity functions sensitivity-difference A
12.4* The Riemann sphere vinnecombe-sphere A
12.5* Stability margins sensitivity-maxpm A
12.6 idealbode-margins A
12.7* Fractional loop transfer function idealbode-fracsys A
12.8* Smith predictor smith-predictor A
12.9* Ideal delay compensator delay-compensation A
12.10* Vehicle steering steering-nyquist A
12.11* Design with dominant pole specification design-fourthord A
12.12* AFM nanopositioning system afm-robustpid A
12.13* $H_\infty$ control hinf-singval A
12.14* Vinnicombe metric computation hinf-vinnecombe A Solution consists of a citation
12.15* Robustness of an observer-based design robust-statespace A Solution is very long
12.16* Robustness using the Nyquist criterion robust-nyquist P Missing figures
12.17 Robustness inequalities robustness-conditions
12.18 vinnecombe-nonunity
12.19 vinnecombe-onepole
12.20 Disk drive tracking missing