2005-03-15 Miroslav Fikar * chappred3.tex (Calculation of the Optimal Control): equation (5.3.20) has no formula with it - deleted 2005-03-12 Miroslav Fikar * chappred5.tex (Derivation of CRHPC, (5.5.8), p. 221): added reference to the matrix inversion lemma: The block matrix inversion formula states -> The block matrix inversion formula states (see its proof of Lemma~\ref{thm:id:invers} on page~\pageref{thm:id:invers}) * chappred5.tex (Derivation of CRHPC, (5.5.8), p. 221): Incorrect sign in the element (2,2) of the inverse matrix: -\Delta -> \Delta \begin{equation} \left( \begin{array}{cc} A^{-1} & D \\ C & B \end{array} \right)^{-1} = \left( \begin{array}{cc} A+ AD\Delta CA & -AD \Delta\\ -\Delta CA & -\Delta \end{array} \right),\quad \Delta^{-1} = B - CAD \end{equation} -> \begin{equation} \left( \begin{array}{cc} A^{-1} & D \\ C & B \end{array} \right)^{-1} = \left( \begin{array}{cc} A+ AD\Delta CA & -AD \Delta\\ -\Delta CA & \Delta \end{array} \right),\quad \Delta^{-1} = B - CAD \end{equation} 2005-03-09 Lubos Cirka * chappred3.tex (Derivation of the Predictor from State-Space Models): (5.3.53) and (5.3.54): matrix C must be inside: \begin{equation} \ve{G} = \ve{\bar{C}} \begin{pmatrix} \ve{\bar{B}} & \ve{0} & \ldots & \ldots & \ve{0} \\ \ve{\bar{A}\bar{B}} & \ve{\bar{B}} & \ve{0} & \ldots & \ve{0} \\ \vdots & & \ddots & \ddots & \vdots \\ \vdots & & & \ve{\bar{B}} & \ve{0} \\ \ve{\bar{A}}^{N_2-1}\ve{\bar{B}} &\ldots & & \ldots & \ve{\bar{B}} \\ \end{pmatrix} \end{equation} and \begin{equation} \ve{y}_0 = \ve{\bar{C}} \begin{pmatrix} \ve{\bar{A}} \\ \ve{\bar{A}}^2 \\ \vdots \\ \ve{\bar{A}}^{N_2} \end{pmatrix} \ve{\bar{x}}(k) \end{equation} -> \begin{equation} \ve{G} = \begin{pmatrix} \ve{\bar{C}\bar{B}} & \ve{0} & \ldots & \ldots & \ve{0} \\ \ve{\bar{C}\bar{A}\bar{B}} & \ve{\bar{C}\bar{B}} & \ve{0} & \ldots & \ve{0} \\ \vdots & & \ddots & \ddots & \vdots \\ \vdots & & & \ve{\bar{C}\bar{B}} & \ve{0} \\ \ve{\bar{C}\bar{A}}^{N_2-1}\ve{\bar{B}} &\ldots & & \ldots & \ve{\bar{C}\bar{B}} \\ \end{pmatrix} \end{equation} and \begin{equation} \ve{y}_0 = \begin{pmatrix} \ve{\bar{C}\bar{A}} \\ \ve{\bar{C}\bar{A}}^2 \\ \vdots \\ \ve{\bar{C}\bar{A}}^{N_2} \end{pmatrix} \ve{\bar{x}}(k) \end{equation} 2005-02-03 Miroslav Fikar * chap53.tex (p. 29_3, Example 1.3.3, section{Discrete-Time Transfer Functions}): T_s + 2 -> T_s + 1 \begin{equation*} G(s)=\frac{Z_2}{(T_1s+1)(T_2 s+2)},\qquad T_1\ne T_2 \end{equation*} -> \begin{equation*} G(s)=\frac{Z_2}{(T_1s+1)(T_2 s+1)},\qquad T_1\ne T_2 \end{equation*} 2005-02-03 Martin Herceg * chap53.tex (p. 30^6-30^9, Example 1.3.3, section{Discrete-Time Transfer Functions}): b1, b2, a1, a2 \begin{eqnarray*} b_1 & = & Z_2 T_1 T_2 \left[-\left(e^{-\frac{T_s}{T_1}} + e^{-\frac {T_s}{T_2}}\right) -\frac{T_1(1+e^{-\frac{T_{s}}{T_{2}}})}{T_2-T_1} +\frac{T_2(1+e^{-\frac {T_{s}}{T_{1}}})}{T_2-T_1} \right]\\ b_2 & = & Z_2 T_1 T_2 \left[ e^{-\frac{T_s}{T_1}} e^{-\frac{T_s}{T_2}} +\frac{T_1e^{-\frac{T_s}{T_2}}}{T_2-T_1} - \frac{T_2e^{-\frac{T_s}{T_1}}}{T_2-T_1} \right] \\ a_1 & = &-\left(e^{-\frac{T_s}{T_1}} + e^{-\frac{T_s}{T_1}}\right)\\ a_2 & = & e^{-\frac{T_s}{T_1}} e^{-\frac{T_s}{T_1}} \end{eqnarray*} -> \begin{eqnarray*} b_1 & = & Z_2 \left[-\left(e^{-\frac{T_s}{T_1}} + e^{-\frac {T_s}{T_2}}\right) -\frac{T_1(1+e^{-\frac{T_{s}}{T_{2}}})}{T_2-T_1} +\frac{T_2(1+e^{-\frac {T_{s}}{T_{1}}})}{T_2-T_1} \right]\\ b_2 & = & Z_2 \left[ e^{-\frac{T_s}{T_1}} e^{-\frac{T_s}{T_2}} +\frac{T_1e^{-\frac{T_s}{T_2}}}{T_2-T_1} - \frac{T_2e^{-\frac{T_s}{T_1}}}{T_2-T_1} \right] \\ a_1 & = &-\left(e^{-\frac{T_s}{T_1}} + e^{-\frac{T_s}{T_2}}\right)\\ a_2 & = & e^{-\frac{T_s}{T_1}} e^{-\frac{T_s}{T_2}} \end{eqnarray*} 2005-01-11 Martin Herceg * chappred7.tex, p.229, Fig. 5.7.1: N1 -> N2 2005-01-05 Martin Herceg * chappred3.tex (subsection{Closed-loop Relations}): p. 218, (5.3.40)] missing term: &=& C \frac{ A\Delta + \sum_{j=N_1}^{N_2} k_j z^{j-1}(B-G_j)}{\sum_{j=N_1}^{N_2} k_j} change for &=& C \frac{ A\Delta + \sum_{j=N_1}^{N_2} k_j z^{j-1}(B - A\Delta G_j)}{\sum_{j=N_1}^{N_2} k_j} 2004-11-17 Miroslav Fikar * chap54.tex (section{Input-Output Discrete-Time Models -- Difference Equations}), p30, (1.4.6): delete $q^{-d}()$: B(q^{-1})=q^{-d}(b_1q^{-1}+b_2q^{-2} + \cdots + b_m q^{-m}) change for B(q^{-1})=b_1q^{-1}+b_2q^{-2} + \cdots + b_m q^{-m} 2004-11-14 Miroslav Fikar * chap52.tex (subsubsection*{Partial Fraction Expansion}), example 1.2.1., p26_3: added material before: \begin{equation*} f(kT_{s)}=\frac{5}{3}\left(1-e^{-0,916k}\right), \qquad k=0,\, 1,\, 2,\, \ldots \end{equation*} new: \begin{equation*} f(kT_{s)}=\frac{5}{3}\left(1-e^{-0,916k}\right) = \frac{5}{3}\left(1-\left(\frac{2}{5}\right)^k \right), \qquad k=0,\, 1,\, 2,\, \ldots \end{equation*} * errata.tex: created file for changes in the manuscript 2004-11-09 Miroslav Fikar * Book printed. New log starts.