Solutions

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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.

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) 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* Occular motion eyemotion C KJA
1.2* Feedback examples fbkexamps C Misc
1.3* Human balance balance-human C CL
1.4* Cruise control redesign cruise-redesign C CL
1.5* Integral action integral C KJA
1.6* Popular press articles nytexamps
1.7 Milk supply chain milksupply P KJA Figure missing
1.8 MATLAB cruise control cruise-mlintro P CL Preliminary solution available; could be cleaned up. Make sure to use Ch 3.1 model
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 P
2.3* Disrete-time dynamics discrete-solutions P
2.4* Keynesian economics discrete-keynes C SH
2.5* Least squares system identification sysid-leastsq I SH
2.6* Normalized oscillator dynamics oscillator P
2.7* Electric generator powergrid P
2.8* Admission control for a queue queue-admcontrol P
2.9* Biological switch biocircuits-switchmod P
2.10* Motor drive dcmotor-modeling P
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 I CL
3.2 Bicycle dynamics bicycle-statespace
3.3 Bicycle steering bicycle-steering
3.4 Operational amplifier circuit opamp-twopole P
3.5 Operational amplifier oscillator opamp-osc P
3.6 Congestion control using RED~\cite{Low+02:infocom} congctrl-red P
3.7 Atomic force microscope with piezo tube afm-preload P
3.8 Drug administration drugadmin-alcohol
3.9 Population dynamics logistic
3.10 Fisheries management fishery-modeling P
3.11 powertrain P

Chapter 4 - Dynamic Behavior

Num Title Filename Stat Auth Comments
4.1 Time-invariant systems timeshift
4.2 Flow in a tank tank-modeling P
4.3 Cruise control cruise-phaseplot P CL Solution available; update if needed to match dynamics in text
4.4 Lyapunov functions lyap-secord P
4.5 Damped spring--mass system lyap-oscillator P
4.6 Electric generator missing P
4.7 Lyapunov equation missing
4.8 Congestion control congctrl-lyapstab P
4.9 Swinging up a pendulum invpend-swingup P
4.10 Root locus diagram missing P
4.11 Discrete-time Lyapunov function discrete-lyapunov
4.12 Operational amplifier oscillator opamp-oscnl P
4.13 Self-activating genetic circuit biocircuits-posfbk P
4.14 Diagonal systems missing P
4.15 Furuta pendulum furuta P
4.16 Routh-Hurwitz criterion routh
4.17 missing
4.18 missing P
4.19 predprey-limit 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
4.24 Steering dynamics of a ship tanker-dynamics P
4.25 Pitchfork bifurcation missing
4.26 stabexmp-mooregreitzer P
4.27 cruise-lyapunov P CL Check to make sure dynamics match Ch 3
4.28 lyapexmp P

Chapter 5 - Linear Systems

Num Title Filename Stat Auth Comments
5.1* Response to the derivative of a signal dersys I SH
5.2* Impulse response and convolution impulse-response I SH
5.3* Pulse response for a compartment model compartment-pulse
5.4* Matrix exponential for second-order system matrixexp P
5.5* Lyapunov function for a linear system lyap-linear I SH
5.6* Nondiagonal Jordan form missing P
5.7* Rise time for a first-order system risetime-firstord I SH
5.8* Discrete-time systems discrete-linsys P
5.9* Keynesian economics discrete-keynes I SH
5.10* missing P
5.11* Transcriptional regulation biocircuits-negfbk 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 P
5.19 State variables in compartment models compartment-states
5.20 queue-linsys P
5.21 Keynes model in continuous time missing
5.22 cartpend 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 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 P
6.13 Atomic force microscope missing
6.14 missing P
6.15 Bryson's rule brysons-rule
6.16 integral-refgain
6.17 Unreachable compartment model compartment-nonreach 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 P
7.5 Integral action integral-action P
7.6 Vectored thrust aircraft pvtol-ssctrl P
7.7 Uniqueness of observers missing
7.8 Observers using differentiation diff
7.9 Observer for Teorell's compartment model compartment-teorellobs P
7.10 Observer design for motor drive dcmotor-observer P
7.11 Feedforward design for motor drive dcmotor-feedforward P
7.12 Whipple bicycle model bicycle-whipple
7.13 Discrete-time random walk kalman-randomwalk P
7.14 Kalman decomposition missing
7.15 missing
7.16 Balance system balance-observable
7.17 Balance system with biased measurement balance-statectrl
7.18 Duality missing
7.19 Balance system missing
7.20 Trajectory generation trajgen-scalar
7.21 Selection of eigenvalues missing
7.22 Kalman filter for scalar ODE kalman-scalar P

Chapter 8 - Transfer Functions

Num Title Filename Stat Auth Comments
8.1 missing
8.2 modalinput P
8.3 Inverted pendulum invpend-xferfcn P
8.4 Solutions corresponding to poles and zeros missing P
8.5 Operational amplifier opamp-pictrl 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 P
8.11 Common poles missing
8.12 Congestion control congctrl-xferfcns P
8.13 Inverted pendulum with PD control invpend-pzcancel P
8.14 Vehicle suspension~\cite{hedrick90} vehicle-quartercar
8.15 Vibration absorber missing P
8.16 freqexamps P
8.17 model-simplification
8.18 cruise-pictrl P Needs to be updated to use model from Ch 3; not yet committed to repository
8.19 dcmotor-xferfcn
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 P
9.2 Atomic force microscope afm-tapping
9.3 Heat conduction missing P
9.4 Vectored thrust aircraft pvtol-looptf 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 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 P
9.15 Congestion control using TCP/Reno congctrl-margins
9.16 opamp-routh P
9.17 missing P
9.18 Limitations missing
9.19 Limitations missing
9.20 Delay differential equations delayde P
9.21 Cruise control design cruise-pictrl P 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 missing
10.2 missing
10.3 missing P
10.4 Ziegler--Nichols tuning missing P
10.5 Vehicle steering steering-pi P
10.6 Congestion control congctrl-pituning P
10.7 Motor drive dcmotor-pdctrl 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 P
10.13 pidexmps P
10.14 Compartment model compartment-monotone
10.15 missing P
10.16 pirlocus P
10.17 pvtol-pid P
10.18 Ball and beam missing
10.19 balance-pid 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 P
11.16 Rear-steered bicycle bicycle-rearsteer P
11.17 missing P
11.18 Rise-time/bandwidth product missing
11.19 missing P
11.20 znlimits
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 P
11.26 secord-rhpz 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 P
11.30 Control of a magnetic levitation system maglev P
11.31 missing P
11.32 pvtol-gangof4

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