Flight Dynamics & Control toolbox: known problems

Known problems

After the toolbox was made public, I received many useful comments and suggestions from several users. The most important problems encountered so far have been listed on this page; recent additions are highlighted in red. If you encounter other problems or bugs, please let me know. Any newly discovered problems will be published here, and from time to time I may publish an updated version of the software to solve the most important bugs.

The FDC 1.3 bugs will be squashed in the next version of the toolbox, FDC 1.4. An early 'beta' of FDC 1.4 is available via CVS. Since I will not describe known bugs for the CVS version on this page, it is very important to update your local CVS tree frequently to stay up-to-date. Your feedback is highly appreciated!

See also the Frequently Asked Questions.

FDC 1.3

The latest release is FDC 1.3.3, which is functionally identical to FDC 1.3 'Service Release 2', but which features different licensing terms. Service Release 2 fixed some problems from the two earlier versions (SR1 and FDC 1.3). If you still use the original FDC 1.3 version, it is strongly recommended to upgrade. Users of FDC 1.3 Service Release 1 can choose to upgrade or to apply the necessary changes manually. Users of Service Release 2 only need to upgrade to FDC 1.3.3 if they require the new licensing terms.

To verify which version you are currently using, check the first line of readme1.txt in the FDC subdirectory doc: the original version was called 'FDC 1.3', Service Release 1 was called 'FDC 1.3 SR1', Service Release 2 was called 'FDC 1.3 SR2', and the latest version is called FDC 1.3.3.

Known problems for all FDC 1.3 releases:

The load and save routines as present in several FDC programs are not able to handle spaces in filenames. Currently, the best work-around is to place the FDC directory in a path that doesn't contain any spaces. FDC 1.4 will feature support for filenames with spaces.
The HTML helpfiles are not exactly free from errors: at certain places the copying and pasting remains are still a little too obvious... If there is any doubt, please consult the FDC user-manual instead. Even though the manual was written for FDC 1.2, its block-reference is still more accurate than the HTML documentation, as it has been verified more thoroughly.
The support for Simulink libraries has been implemented only partially in FDC 1.3: not all blocks from the Simulink systems have been properly linked to these libraries. If you want to edit a block in a system, always check whether or not it is contained in a library. If a library link exists, edit the block inside the library. If not, copy the block from the library to the system, then follow the link back to the library for editing. (As always, first unlock the library before editing.)
Due to the extended warning messages in Matlab 5 and higher, some programs may issue warnings where Matlab 4.2 would ignore them. However, in general this has no consequences for the computed results. Work-around: disable the warnings during program execution by putting a warning off command just below the program header and a warning on command at the end of the program. (This problem has probably been solved in FDC 1.3, Service Release 2, but if it does happen at least you know where it comes from.)
The Pitch Attitude Hold (PAH) mode of the 'Beaver' autopilot systems APILOT1, APILOT2, and APILOT3 contains a washout filter, which is used if the PAH mode acts as 'inner-loop' for the Altitude Hold, Altitude Select, and Glideslope modes. Although the filter itself has been implemented correctly, the location of the block-title 'washout filter' is wrong and therefore quite confusing. In the current lay-out, this title has been put underneath the transfer function-block Kd/s+Kd, which is in fact only part of the complete washout filter s/s+Kd. The actual output of the washout filter consists of the sum of the output from Inport number 4 and the negative of the output from the transfer function Kd/s+Kd (the sign of this signal is changed in the next Sum block). Since Service Release 2, the block-title has been altered slightly to reflect this situation, but that is only a partial work-around for this problem.
The implementation of the turn-coordination in the systems RAH and PAHRAH is incorrect: the signal Kr*(g/V)*sin(φ) must not be multiplied with φ itself! To correct this, the signal line to the second input of the Multiplication block (that is located directly above the 'Turn-coordination' text) and the Multiplication block itself must be removed, leaving only the Kr*(g/V)*sin(φ) signal to be connected to the Sum block.
The Mode Controller block in the systems APILOT2 and APILOT3 causes a data-type mismatch in Matlab R13 (probably also in R12), which is caused by the logical expressions in the blocks "GS mode active?", "NAV mode active?", and "LOC mode active?" producing an output of type boolean instead of double. The reason why these logical expressions were implemented in the first place was to make it clear that these blocks each produce a test signal that functions as a switch. Simply replacing e.g. the expression ymod2S(5)==1 in the block "GS mode active?" by ymod2S(5) should work too and solve the type mismatch. If you want the test to remain clearly visible, replace the logical expression by double(ymod2S(5)==1) instead. Obviously, similar changes need to be made to the other two logical expressions.
Mode switching for the Glideslope mode seems to be taking place too soon because the mode-switching bracket is set too wide. The mode should switch from 'armed' to 'coupled' when the aircraft crosses the glideslope reference line for the first time; this is tested in line 38 of the function gsswitch.m: if abs(u(1)) < 0.005, where 0.005 is a bracket around the nominal value 0. This bracket is needed to account for the numerical simulation steps which make it virtually impossible that the input signal u(1) will ever be identical to zero during a simulation. The bracket can be narrowed by using a smaller test value, such as 0.002 or 0.001. However, if the bracket is set too small, the aircraft may not capture the glideslope at all. A cleverer switching logic will be developed for the next FDC version.
The C-matrix of the linear system block that implements the actuator and cable dynamics for the aileron channel must be multiplied by 2. This has been implemented properly in the APILOT systems, but not in the RAH and PAHRAH models. To update the latter two systems, find the block 'ailerons actuator and cables' in the subsystem 'cable & actuator dynamics', and replace the parameter Cail by Cail*2. (This multiplication factor will be removed in FDC 1.4, which will get updated datamatrices.)
The differentiating filters used in the ILS blocks of APILOT2 and APILOT3 are incorrect; instead of 1/s+1 the transfer function must be set to s/s+1. It is also possible to replace these filters by a 'Derivative' block, except this is not recommended for APILOT3 due to the introduction of ILS noise; the filters approximate a derivative signal, filtering out high-frequency noise.
The block 'Nominal ILS signals' in the APILOT2/ILS and APILOT3/ILS subsystems inadvertently uses the default values of the ILS parameters, as used in the NAVLIB library. Because of this, setting the ILS parameters by clicking the APINIT button (or running APINIT or ILSINIT from the command-line) will not work. To restore the intended behavior, it is necessary to change the respective block-parameters in APILOT2 and APILOT3 as follows:
- Heading of runway: psiRW
- Runway position: [xRW, yRW, HRW]
- X-distance from threshold to localizer antenna: xloc
- X-distance from threshold to glideslope antenna: xgs
- Y-distance from centerline to glideslope antenna: ygs
- nominal glideslope angle: gamgs
All variables are case-sensitive!. Note: FDC 1.2 does not contain this bug. I thank Scott Poll for making me aware of this problem.
For sake of completeness, it is also necessary to change the last block-parameters for 'Glideslope steady state errors' and 'Localizer steady state errors' in APILOT2/ILS and APILOT3/ILS, so that these blocks will also use the settings from APINIT, instead of the default values. 'Nominal glideslope elevation angle' must be changed to gamgs, and 'Distance from runway threshold to LOC antenna' must be set to xloc. Please notice that the error percentages have been set to a default value of zero, which means that this error normally will not affect the results. Only if the percentages are changed manually (contrary to the other ILS parameters, the error percentages are not not defined by APINIT or ILSINIT!) will the influence of this bug become noticeable, and even then the overall effect will remain small. FDC 1.2 does not contain this bug.
A similar problem occurs in the block 'Nominal VOR signals' in the APILOT2/VOR and APILOT3/VOR subsystem. Here, the block parameters should be set to:
- X-position of VOR station: xVOR
- Y-position of VOR station: yVOR
- Altitude of VOR station: HVOR
- Course Datum: CD
Again: these variables are case-sensitive. Note: FDC 1.2 does not contain this bug.
Line 58 of ilsinit.m is incorrect. Instead of: Sgs=625/abs(gamgs);, the line should be: Sgs=625/abs(gamgs*pi/180);. This affects the 1/Sgs gains in the ILS blocks of APILOT2 and APILOT3; the Sgs gain in the block 'Nominal ILS signals' is correct, as those are determined in the mask initialization lines.
The utility SYSTPROP should be able to accept only the A, B, and C matrices of a linear state-space model as input arguments if all elements of the D matrix are zero. Unfortunately, this does not work, due to an error in the (automatic) sizing of D. The easiest work-around is to always specify D as fourth input argument. Since the option to leave out D wasn't documented anyway, I doubt if anyone have ever used it.
The turbulence blocks and ILS/VOR noise blocks use a Simulink White Noise block, which are in fact not suitable for continuous-time systems. It is recommended to replace these blocks by Band-limited White Noise blocks instead. Please be sure to use different seed values for the longitudinal, lateral, and vertical turbulence blocks, to ensure that these signals will be truly independent of eachother. Furthermore, Noise Power 1.0 and default sample time seem to work fine. (Notice that the sample time must be much smaller than the fastest dynamics of the system to obtain accurate simulations. The Simulink helpfile gives the following guideline: ts = 0.01*(2*pi/fmax) where ts is the sample time and fmax is the bandwidth of the system in rad/sec.)
The load routine in INCOLOAD and the save routines in ACTRIM and ACLIN cannot handle filenames and/or directory names containing spaces. Although a crude work-around for INCOLOAD was posted here earlier, I have removed this as I found that the problem extended to ACTRIM and ACLIN as well. The upcoming version FDC 1.4 (of which a beta is currently available via CVS) will fix this problem permanently. For earlier FDC versions, the best work-around is to install the toolbox in a path that doesn't contain any spaces, and to refrain from using spaces in filenames and directories when creating or retrieving files with utilities from the FDC toolbox.
The equations used in the blocks BLWIND and CWIND are valid only if the aircraft's X and Y body-axes are oriented in a horizontal plane with respect to the Earth and the vertical wind component is disregarded. As a consequence, both blocks are of limited value only; it is planned to include a complete axis-transformation block in a future version of the toolbox.
While RESULTS allows the user to select different units for angular values ([rad] or [deg]) and angular rates ([rad/s] or [deg/s]), RESPLOT will always use [deg] and [deg/s] for its plot labels. A quick-and-dirty solution for this problem is to include the following code immediately after the first comment lines (thanks to Yongliang Chen for the suggested changes):

global c1, c2; % Here c1 and c2 are created by RESULTS.M if c1==1    unit_angle='[rad]'; else    unit_angle='[deg]'; end if c2==1    unit_rate='[rad/s]'; else    unit_rate='[deg/s]'; end
and change the ylabel designations for the affected plots as in:
   ylabel(['attack angle alpha ' unit_angle]);
and:
   ylabel(['roll rate p ' unit_rate]);.
The SYSTPROP code for determining the overshoot in lines 188-190 does not cater for all possible combinations of dynamics. Please replace these lines by the following code to rectify this problem (thanks to Yongliang Chen for the suggested changes):

% Determine the overshoot percentage if prop(i,5) > 0 & prop(i,5) < 1; % damped oscillatory prop(i,6) = 100*exp(-pi*prop(i,5)/sqrt(1-prop(i,5))); elseif prop(i,5) > 1; % non-oscillatory and stable prop(i,6) = 0; else prop(i,6) = inf; % unstable end
The indices in line 276 of SYSTPROP are incorrect: all n indices must be replaced by i,
i.e. prop(n,6) must become prop(i,6), and so on. Thanks to Yongliang Chen for pointing this out.
FDC 1.3 has not been tested with Matlab 5.2 / Simulink 2.2, but tests with Matlab 5.3 / Simulink 3.0 proved to be successful. Given earlier experiences with Matlab upgrades, there may be problems with newer Matlab versions whenever they become available. According to an independent user report, the toolbox works fine with Matlab 6 / Simulink 4 also. However, please read the FAQ-section about 'slupdate'.

Known problems for FDC 1.3 and FDC 1.3 SR1 only:

Line 646 of actrim.m should be vtrim = vtrimmed; to prevent an infinite loop from occurring when the maximum number of iterations is exceeded.
The input line for the flightpath angle gamma in actrim.m doesn't contain the necessary conversion from degrees to radians. To correct this, change line 323 of this program as follows:
gamma = input('Give flightpath angle [deg], default = 0: ')*pi/180;
The parameter sequence for the call to the function FMINS in actrim.m and trimdemo.m is incorrect: the variable options must be replaced by the empty matrix [ ], and vice versa. Furthermore, in trimdemo.m the variables xinco and xfix need to be defined at the top of the program (suitable values are xinco=[45,zeros(0,11)]' (notice the transpose sign!), and xfix=1).
In the Heading Hold, Altitude Select, and Altitude Hold subsystems from the autopilot models, the Inport blocks Dpsir, DHdot, and DHr are drawn with both a white foreground and a white background color, which renders these blocks invisible. The easiest work-around is to change the background color to light-blue to make these blocks visible again. It is recommended to change the foreground color of these Inports to black, their background color to orange, and reset the screen color back to white, in order to get a more consistent color scheme.
The path-separator ' ; ' is applied instead of the generic path-separator pathsep on lines 427, 450, and 452 of fdcinit.m. In fdchelp.m a backslash ( ' \ ' ) is used instead of filesep on line 34.
To work in UNIX, line 35 of fdchelp.m needs to be changed to:
browsercall=['web file:' filename ';'];
(this change does not affect performance under Windows).
On line 313 of modbuild.m the DOS delete-command is applied instead of the more generic delete('modbuild.tmp');.
My decision to keep the directory-names in upper case for Service Release 1 was not such a good idea after all, as some M-files defined the subdirectories in lower case characters. It is possible to alter these M-files, but it is easier to rename all FDC directories to lower case.

One suggestion that will at least partly solve the upper/lowercase problems is to substitute line 448 of fdcinit.m:
pos = findstr(matlabpath,rootdir);
with the lines:
if computer=='PCWIN', pos = findstr(lower(matlabpath),lower(rootdir)); else pos = findstr(matlabpath,rootdir); end
Nevertheless, this version has considerably less problems with upper/lowercase characters in filenames than the original FDC 1.3 release.

Known problems for the original FDC 1.3 release only:

The application of DOS-based file-separators and inconsistent use of upper and lower-case characters in filenames and HTML links caused many problems in non-Windows environments. Because of this, virtually all links in the HTML helpfiles proved to be invalid for non-Windows computers.
The HTML helpfiles didn't look good on most computers due to poor font-declarations (font-sizing and font-types).
The HTML help-file refsgnls.htm was missing.

If you still use the original FDC 1.3 release, it is strongly recommended to upgrade to version 1.3.3 or newer. Notice that the above list of problems for the original FDC 1.3 release is not complete; it is merely a short summary.

FDC 1.2

FDC 1.2 is still available as separate download to satisfy Matlab 4.x users. This version is no longer being actively developed, and the known bugs will not be fixed. This version of the toolbox is not compatible with Matlab 5 / Simulink 2 or newer.

The latest release of FDC 1.2 is FDC 1.2.1. It incorporates some small improvements that were previously distributed in a separate file UPDATE.ZIP, and is now distributed under open source license terms.

Several users who tried to run FDC 1.2 on non-Windows platforms have complained about setup-problems, caused by the use of DOS path-names in the setup routine fdcinit.m. Modifying this routine for non-Windows platforms can be rather time-consuming and cumbersome. Work-around: replace fdcinit.m by a custom program that enhances the Matlab path with the FDC 1.2 directories (including all subdirectories). Call this program each time before starting FDC 1.2, or alternatively: each time during the Matlab startup. Note: according to a Mac-user the Matlab path will automatically be enhanced with the FDC directories if you put the FDC toolbox in a subdirectory of matlab/toolbox. However, this does not work on Windows computers, and I haven't verified it on a Mac myself.
The use of DOS path-names also affects routines which define path-names for data files. The affected Matlab programs are: aclin.m, actrim.m, datadir.m, aclin.m, incoload.m, loader.m, fdcdir.m, and setdir.m (note: if the UPDATE.ZIP package has been installed, some of these routines are not affected). Work-around: replace the DOS path-separator '\' (backslash) by the path-separator for the desired computer platform. Unfortunately, Matlab 4.x does not yet feature generalized path-separators.
In the programs aclin.m and modbuild.m temporary files are deleted by means of the command: dos('del [filename]'). This command must be adapted for non-Windows computers.
Line 646 of actrim.m should be vtrim = vtrimmed; to prevent an infinite loop from occurring when the maximum number of iterations is exceeded.
The input line for the flightpath angle gamma in actrim.m doesn't contain the necessary conversion from degrees to radians. To correct this, change line 323 of this program as follows:
gamma = input('Give flightpath angle [deg], default = 0: ')*pi/180;
The call to the function FMINS in ACTRIM and TRIMDEMO may have a wrong parameter sequence: the variable 'options' and the empty matrix [ ] may have to be exchanged (I don't know for sure, because there may be a difference in function parameters for Matlab 4.x and Matlab 5.x).
The utility SYSTPROP should be able to accept only the A, B, and C matrices of a linear state-space model as input arguments if all elements of the D matrix are zero. Unfortunately, this does not work, due to an error in the (automatic) sizing of D. The easiest work-around is to specify D as fourth input argument, regardless of its value. Since the option to leave out D wasn't documented anyway, I doubt if anyone have ever used it.
Before running TRIMDEMO, it is necessary to load the aircraft parameters with load aircraft.dat -mat, and to define the initial value of xinco and xfix (suitable values are xinco=[45,zeros(0,11)]' and xfix=1).
The load and save routines as present in several FDC programs are not able to handle spaces in filenames. Currently, the best work-around is to place the FDC directory in a path that doesn't contain any spaces. FDC 1.4 will feature support for filenames with spaces (however, it will require a newer Matlab/Simulink combo).
The equations used in the block CWIND are valid only if the aircraft's X and Y body-axes are oriented in a horizontal plane with respect to the Earth and the vertical wind component is disregarded. As a consequence, it is of limited value only; it is planned to include a complete axis-transformation block in a future version of the toolbox.
The differentiating filters used in the ILS blocks of APILOT2 and APILOT3 are incorrect; instead of 1/s+1 the transfer function must be set to s/s+1. It is also possible to replace these filters by a 'Derivative' block, except this is not recommended for APILOT3 due to the introduction of ILS noise; the filters approximate a derivative signal, filtering out high-frequency noise.
Line 58 of ilsinit.m is incorrect. Instead of: Sgs=625/abs(gamgs);, the line should be: Sgs=625/abs(gamgs*pi/180);. This affects the 1/Sgs gains in the ILS blocks of APILOT2 and APILOT3; the Sgs gain in the block 'Nominal ILS signals' is correct, as those are determined in the mask initialization lines.
The implementation of the turn-coordination in the systems RAH and PAHRAH is incorrect: the signal Kr*(g/V)*sin(φ) must not be multiplied with φ itself! To correct this, the signal line to the second input of the Multiplication block (that is located directly above the 'Turn-coordination' text) and the Multiplication block itself must be removed, leaving only the Kr*(g/V)*sin(φ) signal to be connected to the Sum block.
The C-matrix of the linear system block that implements the actuator and cable dynamics for the aileron channel must be multiplied by 2. This has been implemented properly in the APILOT systems, but not in the RAH and PAHRAH models. To update the latter two systems, find the block 'ailerons actuator and cables' in the subsystem 'cable & actuator dynamics', and replace the parameter Cail by Cail*2.

FDC documentation

The FDC report was primarily written for version 1.2; there is no dedicated FDC 1.3 manual. The differences between these two versions primarily concern some minor user-interface upgrades, new self-explaining on-line helpfiles, and Matlab 5 compatibility issues; the basic structure of the toolbox hasn't changed. Therefore, the FDC 1.2 documentation can be used for both current FDC versions.

Since May 11, 2001, the second edition of this FDC report is available for download. This second edition features improved graphics and is available as resolution-independent PostScript (PS) and PDF files, whereas the first edition was available in PostScript only and limited to 300 dpi quality. The new version also solves some small technical problems with the report files, except for the following small problem:

The report was designed for A4 paper, which is slightly longer than the US 'letter' format. You may loosse some pagenumbers from the reference sections when printing out the report on a 'letter' format paper, but all other relevant information will fit.

In theory, it is still possible that copies of the first edition are distributed by third parties. If you already have a hard-copy of the report, it is not very useful to download the new edition, but it is recommended to download the new version if you obtained the old version of the report as a ZIP-archive. The first edition of the report was distributed as REPORT.ZIP, whereas the second edition is distributed as REPORT_PS.ZIP, or REPORT_PDF.ZIP, depending on the chosen file format. If your version is called REPORT.ZIP, it is recommended to download a new copy here.

Errata for the FDC 1.2 user-manual:

The License Agreement in chapter 1.3 has become obsolete. Please refer to the software documentation instead for the current information, or take a look at the License Agreement page on this site.
The typographical conventions described in the Preface are not always applied consistently and correctly. This is especially true for matrices, which are often denoted in bold capitals instead of normal-weight capitals only.
Equation (3.12) is not entirely accurate: in fact, the pre-multiplication term d is a diagonal matrix instead of a vector. Note: the block FMDIMS in the toolbox uses the pre-multiplication matrix q_dyn·S·diag([1 1 1 b cbar b]), whereas equation (3.12) uses q_dyn·S·diag([1 1 1 b/2 cbar b/2]). The FMDIMS implementation is in fact correct (thanks to Giampiero Campa for pointing this out).
The engine power P in equation (3.15) has been expressed in [ kW ] instead of [ W ] (or [ N m s^-1 ] as it says in the text). Also a mix-up between BHP (Brake Horse Power) and PS (Pferdestärke or 'continental horse power') seems to have been made, resulting in an underestimation of the engine power by approximately 1.4%. The correct multiplication factor is 0.7457 instead of 0.7355. However, the latter factor has also been used by the FDC software itself, and it should be noted that a difference of 1.4% may well lie within the uncertainty margin of the model parameters themselves.
In step 3 at the end of section 3.2.3 on page 4 the cos(β) term multiplying C_{Y_betadot} is missing. The same error was made in the description of XDOTCORR on page 105. Equation (3.23) and the Simulink implementation of XDOTCORR are correct.
In equation (3.37), the exponent γ/(γ-1) underneath the square root sign should read (γ-1)/γ.
The sign of the cosθcos&phi term in the A_z-equation should be negative; the correct equation is: A_z = a_z,k - cosθcosφ = (F_z - Z_gr)/W. (Thank you Valentin Cristea for your error report.)
Equation (3.49) doesn't seem to be correct. The correct relation between the bank angle Φ, the pitch angle θ, and the roll angle φ according to ref.[23] is: sin(Φ) = sin(φ)·sin(90-θ) = sin(φ)·cos(θ).
Equations (3.51) are valid only if the aircraft's X and Y body-axes are oriented in a horizontal plane with respect to the Earth and the vertical wind component is disregarded. As a consequence, the block CWIND is currently of limited value only. It is planned to include a complete axis-transformation block in a future version of the toolbox.
The entire denominator from equations (3.66) and (3.67) should be squared.
The description of the simulation tools in chapter 4 is based on the old Simulink 1.x versions. Although newer Simulink versions use different methods, chapter 4 may still provide some useful background information.
The 'F' in the denominator of equation (4.19) should be deleted.
The reference to equation (B.60) in the last alinea of section 4.3.2 is incorrect; it should refer to equation (B.59) instead.
In equations (4.43) and (4.53), the second term (x-x₀) should be replaced by (u-u₀).
On page 85, in the 'Equations' section, the units of measurement for the gravitational acceleration g should, of course, be [ms^-2] instead of [ms^-1].
A warning about the DIMLESS block, described on page 86: notice that this block uses multiplication factors cbar/V and b/2V, whereas many other references use factors cbar/2V and b/2V. If you plan to implement 3^rd-party models in the FDC framework, it is very important to be aware of this!
In equations (11.3) and (11.4) the dot is missing above the first Γ_loc.
The turn-coordination loops from figures 11.8 and 11.9 are somewhat ambiguous regarding the adverse yaw suppression (see page 176 for an explanation of that phenomenon): Kr*(g/V)*sin(φ) is not a gain, but a function, where the roll angle φ is the input value. In other words, the output signal from that block equals Kr*(g/V)*sin(φ), not φ *Kr*(g/V)*sin(φ)! These unclear figures were the root cause of the incorrect implementation of the turn-coordination in the systems RAH, and PAHRAH, which has persisted through all versions of the toolbox up till FDC 1.4 'beta' from January 5, 2004.
In table 11.2, (θ_ref – θ) should be replaced by K_θ·(θ_ref – θ). In addition, (φ_ref – φ) should be replaced by K_φ·(φ_ref – φ).
The incorrect turn-coordination loop in the systems RAH and PAHRAH is obviously also reflected in figures 12.3 and 12.5. To correct these diagrams, the signal line to the second input of the Multiplication block (that is located directly above the 'Turn-coordination' text) and the Multiplication block itself must be removed, leaving only the Kr*(g/V)*sin(φ) signal to be connected to the Sum block.
Page 207, PAH mode example, line 9 must be: "Option 4 is not necessary because APILOT1 does not contain ..."
Equation (B.10) on page 228 is missing a V before δm: δM_c.g. = δhdot-(V-V_c.g.)×Vδm = ...
Equation (B.11) incorrectly uses a derivative both inside and outside the sumation of δh. Either remove the dot above δh, or remove the d/dt term that precedes the summation sign.
The referrals to equation (B.28) in the lines above equations (B.38), (B.42), and (B.47) are incorrect; they were meant to refer to equation (B.27) instead.
The last term in equation (B.38) should be F_z*sin(α)*cos(β) instead of F_z*sin(α)*sin(β). The same error was made in the first line of equation (B.54).
In the line above equation (B.54) on page 235, V should be replaced by V_a.

The Flight Dynamics and Control Toolbox