# Difference between revisions of "Solutions"

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

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

### Chapter 1 - Introduction

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

### Chapter 2 - System Modeling

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

### Chapter 3 - Examples

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

### Chapter 4 - Dynamic Behavior

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

### Chapter 5 - Linear Systems

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

### Chapter 6 - State Feedback

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

### Chapter 7 - Output Feedback

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

### Chapter 8 - Transfer Functions

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

### Chapter 9 - Frequency Domain Analysis

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

### Chapter 10 - PID Control

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

### Chapter 11 - Frequency Domain Synthesis

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

### Chapter 12 - Robust Performance

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