2014-11-05 Miroslav Fikar * chap64.tex: Figure 7.12, remove setpoint w from legend 2014-10-23 Miroslav Fikar * chap63.tex: --- chap63.tex.~1~ 2014-10-16 10:23:56.000000000 +0200 +++ chap63.tex 2014-10-23 21:35:50.118977302 +0200 @@ -418,7 +418,7 @@ the steady state is a complex function of parameters, but can be approximated as \begin{equation} - T_{\epsilon} \approx \frac{ \log \left( p \sqrt{1-\zeta^2} \right)}{ + T_{\epsilon} \approx \frac{ \ln \left( p \sqrt{1-\zeta^2} \right)}{ \zeta\omega_0} \end{equation} Maximum overshoot is given by the relation @@ -445,7 +445,7 @@ performance indices and their relations to controller parameters and vice versa. Integral cost function value is inversely proportional to - $\omega_0^2$. Maximum overshoot and all time indices are inversely + $\omega_0^2$. All time indices are inversely proportional to $\omega_0$. Transient response of the closed-loop system to setpoints or disturbances is improved by increasing $\omega_0$. Further, maximum overshoot or damping coefficient 2014-10-16 Miroslav Fikar * chap63.tex: wrong formula for maximum overshoot --- chap63.tex.~1~ 2007-01-29 09:58:22.000000000 +0100 +++ chap63.tex 2014-10-16 10:23:56.000000000 +0200 @@ -423,7 +423,7 @@ \end{equation} Maximum overshoot is given by the relation \begin{equation} - e_{\max} = \E^{-\pi \zeta \sqrt{1-\zeta^2}} = \sqrt{\zeta_d} + e_{\max} = \E^{-\pi \zeta/ \sqrt{1-\zeta^2}} = \sqrt{\zeta_d} \end{equation} and occurs at the time \begin{equation} 2013-11-27 Miroslav Fikar * chap64.tex: typo: tume -> time --- chap64.tex.~1~ 2007-01-29 09:58:22.000000000 +0100 +++ chap64.tex 2013-11-27 10:38:43.000000000 +0100 @@ -1271,7 +1271,7 @@ speaking, Ziegler-Nichols methods have the following in common: \begin{itemize} \item transient responses are fairly oscillatory, -\item not suitable for tume-delay systems, +\item not suitable for time-delay systems, \item difficult tuning. \end{itemize} * chap64.tex untranslated word 2x: Regulator -> Controller --- chap64.tex.~1~ 2013-11-27 10:43:07.000000000 +0100 +++ chap64.tex 2013-11-27 10:41:43.000000000 +0100 @@ -1187,7 +1187,7 @@ sets smaller overshoot, PID$_2$ is underdamped} \label{tab:6znkmit} \begin{tabular}{llll} - Regulator & $Z_R$ & $T_I$ & $T_D$ \\ \hline + Controller& $Z_R$ & $T_I$ & $T_D$ \\ \hline P & $0.5 Z_{Rk}$ & & \\ PI & $0.4 Z_{Rk}$ & $0.8 T_k$ & \\ PID & $0.6 Z_{Rk}$ & $0.5 T_k$ & $0.125 T_k$ \\ \hline @@ -1232,7 +1232,7 @@ \caption{The Ziegler-Nichols controller tuning based on the process step response} \label{tab:6znpch} \begin{tabular}{llll} - Regulator & $Z_R$ & $T_I$ & $T_D$ \\ \hline + Controller& $Z_R$ & $T_I$ & $T_D$ \\ \hline P & $\frac{1}{Z} \frac{T_n}{T_u}$ & & \\ PI & $\frac{0.9}{Z} \frac{T_n}{T_u}$ & $3.33T_u$ & \\ PID & $\frac{1.2}{Z} \frac{T_n}{T_u}$ & $2 T_u$ & $0.5 T_u$ \\ \hline 2013-11-19 Miroslav Fikar * chap22.tex: typo F_1 -> F_2 --- chap22.tex.~1~ 2007-01-29 09:58:20.000000000 +0100 +++ chap22.tex 2013-11-19 20:33:23.489167908 +0100 @@ -141,7 +141,7 @@ \begin{eqnarray} \frac{\dd h_1}{\dt} &=& \frac{q_0}{F_1} - \frac{k_{11}}{F_1} \sqrt{h_1 - h_2} \label{eq:2217} \\ - \frac{\dd h_2}{\dt} &=& \frac{k_{11}}{F_1} \sqrt{h_1 - h_2} + \frac{\dd h_2}{\dt} &=& \frac{k_{11}}{F_2} \sqrt{h_1 - h_2} - \frac{k_{22}}{F_2} \sqrt{h_2} \label{eq:2218} \end{eqnarray} 2013-01-12 Miroslav Fikar * chap55.tex: typo B -> \Gamma --- chap55.tex.~1~ 2007-01-29 09:58:21.000000000 +0100 +++ chap55.tex 2013-01-12 15:30:11.186082379 +0100 @@ -274,7 +274,7 @@ \ve{x}(2) &=& \ve{\Phi}\ve{x}(1) +\ve{\Gamma}\ve{u}(1)\\ %\label{eq:5540} &=& \ve{\Phi}^{2}\ve{x}(0) +\ve{\Phi}\ve{\Gamma}\ve{u}(0)+ - \ve{B}\ve{u}(1) + \ve{\Gamma}\ve{u}(1) \end{eqnarray} Further continuation gives * chap53.tex: improved caption --- chap53.tex.~1~ 2007-01-29 09:58:21.000000000 +0100 +++ chap53.tex 2013-01-12 09:25:15.686173899 +0100 @@ -5,7 +5,7 @@ \centering % \center{\fbox{obr531}} \center{\includegraphics[width=0.7\linewidth,clip]{obr531}} - \caption{Sample-and-hold device in series with a continuous-time system} + \caption{Sampler in series with a continuous-time system} \label{fig:531} \end{figure} 2013-01-07 Miroslav Fikar * chap52.tex: p. 197, (5.36), initial value of the Z-transform --- chap52.tex.~1~ 2013-01-07 13:34:19.275473005 +0100 +++ chap52.tex 2013-01-07 20:22:53.200339377 +0100 @@ -121,7 +121,7 @@ For an initial function value holds \begin{equation} %\label{eq:5217} -\lim_{k\rightarrow 0}f(kT_{s})=\lim_{z\rightarrow \infty}\frac{z-1}{z}F(z) +\lim_{k\rightarrow 0}f(kT_{s})=\lim_{z\rightarrow \infty} F(z) \end{equation} 2012-09-11 Miroslav Fikar * chap43.tex: p. 153, (4.3.11), missing $j$ in denominator 71c71 < +\frac{1}{(\omega^2 T_1^2+1)} \frac{ \E^{\J\omega t} - \E^{-\J\omega t}}{2} --- > +\frac{1}{(\omega^2 T_1^2+1)} \frac{ \E^{\J\omega t} - \E^{-\J\omega t}}{2j} 2012-08-16 Miroslav Fikar * chap31: use environment {proof} consistently in all proofs 2012-04-03 Miroslav Fikar * chappred3.tex: replaced all 't+' by 'k+'. E.g. y(t+1) -> y(k+1) 2012-03-05 Miroslav Fikar * chapopt6.tex (u): Page 350, (8.334): delete minus sign in equation @@ -612,7 +612,7 @@ or \begin{equation} \label{eq:opt0674} - u = - \frac{q(s)}{p(s)}\left( {w - y} \right) + u = \frac{q(s)}{p(s)}\left( {w - y} \right) \end{equation} The choice of $ \tilde {w} $ from~(\ref{eq:opt0672}) changes the closed-loop system in Fig.~\ref{fig:opt065} from a 2012-02-25 Miroslav Fikar * opt065.eps: Fig. 8.17, page 349, change: p(s)/o(s) -> q(s)/o(s) 2012-02-24 Miroslav Fikar * chapopt6.tex: page 342, (8.264) typo CL -> LC \end{pmatrix} &=& \begin{pmatrix} {\ve{A} - \ve{BK}} & {\ve{BK}} \\ - \ve{0} & {\ve{A} - \ve{CL}} + \ve{0} & {\ve{A} - \ve{LC}} \end{pmatrix} \begin{pmatrix} \ve{x}(t) \\ \ve{e}(t) 2012-02-22 Miroslav Fikar * chapopt5.tex, page 338, equations (8.243), (8.244), (8.246), missing transpose @@ -276,7 +276,7 @@ \label{eq:opt0533} \ve{\dot{z}}(t) - \ve{\dot{N}}(t)\ve{\lambda} (t) \\ \mbox{} - \ve{N}(t)\left[ \ve{C}^T\ve{S}^{-1}\ve{y}(t) - - \ve{CS}^{-1}\ve{C}\left( \ve{z}(t) - \ve{N}(t)\ve{\lambda }(t) \right) + - \ve{C}^T\ve{S}^{-1}\ve{C}\left( \ve{z}(t) - \ve{N}(t)\ve{\lambda }(t) \right) - \ve{A}^T\ve{\lambda}(t) \right]\\ = \ve{A}\left[ {\ve{z}(t) - \ve{N}(t)\ve{\lambda}(t)} \right] - \ve{V\lambda}(t) @@ -286,7 +286,7 @@ \label{eq:opt0534} \ve{\dot{z}}(t) - \ve{N}(t)\ve{C}^T\ve{S}^{ - 1}\left( {\ve{y}(t) - \ve{Cz}(t)} \right) - \ve{Az}(t) \\ = \left[ {\ve{\dot{N}}(t) - \ve{N}(t)\ve{A}^T - \ve{AN}(t) - + \ve{N}(t)\ve{CS}^{ - 1}\ve{CN}(t) - \ve{V}} \right]\ve{\lambda }(t) + + \ve{N}(t)\ve{C}^T\ve{S}^{-1}\ve{CN}(t) - \ve{V}} \right]\ve{\lambda }(t) \end{multline} We can choose $\ve{z}(t)$ and $\ve{N}(t)$ such that \begin{eqnarray} @@ -297,7 +297,7 @@ \ve{z}(0) &=& \ve{\bar{x}}_0 \\ \label{eq:opt0538a} \ve{V} &=& \ve{\dot{N}}(t) - \ve{N}(t)\ve{A}^T - \ve{AN}(t) + -\ve{N}(t)\ve{CS}^{ - 1}\ve{CN}(t) \\ +\ve{N}(t)\ve{C}^T\ve{S}^{-1}\ve{CN}(t) \\ \label{eq:opt0537} \ve{N}(0) &=& \ve{N}_0 \end{eqnarray} * chapopt5.tex, page 338, equation (8.236), wrong sign @@ -222,7 +222,7 @@ $\ve{x}(0)$ is free as well and thus \begin{equation} \label{eq:opt0526} -\ve{x}(0) = \ve{\bar {x}}_0 + \ve{N}_0 \ve{\lambda}(0) +\ve{x}(0) = \ve{\bar {x}}_0 - \ve{N}_0 \ve{\lambda}(0) \end{equation} Optimal control follows from the optimality condition 2011-05-23 Miroslav Fikar * chappred3.tex: page 417, equation (9.74) untranslated word from Slovak: inak $\to$ otherwise @@ -648,7 +648,7 @@ \bar{u}(k-i+j)= \left\{ \begin{array}{ll} u_f(k-1) & j \geq i \\ - u_f(k-i+j) & \mbox{inak} + u_f(k-i+j) & \mbox{otherwise} \end{array} \right. \end{equation} 2011-04-25 Miroslav Fikar * chappredex.tex: pages 427/428, equations (9.109a), (9.111a). Small corrections in cost function formulation \begin{subequations} \label{eq:predex:finite_constr2} \begin{align} - I^*(\ve{x}_0) &=\ve{x}_0^T \ve{Y} \ve{x}_0 - + \min_{\ve{U}_N} \frac{1}{2} \bigg\{ \ve{U}_N^T \ve{H} \ve{U}_N + \ve{x}_0 ^T + I^*(\ve{x}_0) &= \frac{1}{2} \ve{x}_0^T \ve{Y} \ve{x}_0 + + \min_{\ve{U}_N} \bigg\{ \frac{1}{2} \ve{U}_N^T \ve{H} \ve{U}_N + \ve{x}_0 ^T \ve{F} \ve{U}_N \bigg\}\\ \text{subj. to } & \ve{G} \ve{U}_N \leq \ve{W} + \ve{E} \ve{x}_0 \end{align} @@ -93,11 +93,12 @@ \begin{subequations} \label{eq:predex:finite_constr3} \begin{align} - I^*(\ve{x}_0) &= \min_{\ve{z}} \frac{1}{2} \bigg\{ \ve{z}^T \ve{H} \ve{z} \bigg\}\\ + I_z^*(\ve{x}_0) &= \min_{\ve{z}} \frac{1}{2} \bigg\{ \ve{z}^T \ve{H} \ve{z} \bigg\}\\ \text{subj. to } & \ve{G} \ve{z} \leq \ve{W} + \ve{S} \ve{x}_0 \end{align} \end{subequations} -where $\ve{S}=\ve{E}+\ve{G}\ve{H}^{-1}\ve{F}^T$. +where $\ve{S}=\ve{E}+\ve{G}\ve{H}^{-1}\ve{F}^T$ and $ I_z^*(\ve{x}_0) += I^*(\ve{x}_0) -\ve{x}_0^T (\ve{Y} - 1/2 \ve{F} \ve{H}^{-1}\ve{F}^T)\ve{x}_0 $. 2010-11-03 Miroslav Fikar * chapopt4.tex (I): page 327, typo: sufficent -> sufficient 2010-07-28 Miroslav Fikar * chappredex.tex: (steps of explicit MPC, page 429) repeated term the the 2009-08-14 Miroslav Fikar * chapad3.tex: page 448, equation (10.1), typo in numerator of transfer function 48c48 < G(s) = \frac{b_{s1} s + a_{s0} }{a_{s2} s^2 + a_{s1} s + 1} --- > G(s) = \frac{b_{s1} s + b_{s0} }{a_{s2} s^2 + a_{s1} s + 1} 2008-06-03 Miroslav Fikar * chap42.tex (subsection{Time Responses of Liquid Storage Systems}): incorrect reference to equation: 347c347 < Substracting~\eqref{eq:4237} from \eqref{eq:4240} yields --- > Substracting~\eqref{eq:4238} from \eqref{eq:4240} yields 2007-09-12 * chap31.tex (subsubsection*{Trigonometric Functions}): wrong sign + -> - 211c211 < +\frac{1}{2\J}\left[\frac{\E^{-(s+\J\omega)t}}{-(s+\J\omega)} --- > -\frac{1}{2\J}\left[\frac{\E^{-(s+\J\omega)t}}{-(s+\J\omega)}