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zHsa#F5g+%21*2eV@lZ@LhzI+a}28`+!1AJ+42AAI49+wvK z_fu95vKg49nBL9wWju0F30_Z1t~HrJgPxLx$AJ}=q7Fcn*|d*Kz3M2XHxJA0$aJx~ zP+{$e-?n(@0&hyo{bt{sH{2`L#x?8qu-%1X_P+O>dP6pR@2BespXUwr z8Z3DZWLKCPsi>q>q~ZS`eW>uk diff --git a/Lab01/report/Work1_report.tex b/Lab01/report/Work1_report.tex index 7505129..cc752c4 100644 --- a/Lab01/report/Work1_report.tex +++ b/Lab01/report/Work1_report.tex @@ -89,7 +89,7 @@ \begin{itemize} \item Την παρούσα αναφορά. \item Τον κατάλογο \textbf{scripts/}, που περιέχει τον κώδικα της MATLAB. - \item Το \href{https://git.hoo2.net/hoo2/SystemModling/src/branch/master/Work%201}{σύνδεσμο} με το αποθετήριο που περιέχει όλο το project με τον κώδικα της MATLAB, της αναφοράς και τα παραδοτέα. + \item Το \href{https://git.hoo2.net/hoo2/SystemModling/src/branch/master/Lab01}{σύνδεσμο} με το αποθετήριο που περιέχει όλο το project με τον κώδικα της MATLAB, της αναφοράς και τα παραδοτέα. \end{itemize} \section{Μοντελοποίηση και Προσομοίωση Συστήματος Εκκρεμούς – Θέμα 1} @@ -187,7 +187,7 @@ \] Στο Σχήμα~\ref{fig:prob2a} παρουσιάζονται η πραγματική και η εκτιμώμενη γωνία, καθώς και το σφάλμα $e_q(t)$ μεταξύ τους. -\InsertFigure{!ht}{1}{fig:prob2a}{../scripts/output/Prob2_20s_Ts0.1.png}{ +\InsertFigure{!ht}{1.05}{fig:prob2a}{../scripts/output/Prob2_20s_Ts0.1.png}{ Αποτελέσματα εκτίμησης παραμέτρων με χρήση όλων των μεταβλητών κατάστασης. } \paragraph*{Συμπεράσματα:} @@ -204,7 +204,7 @@ \] Ακολουθείται η ίδια διαδικασία παλινδρόμησης με την περίπτωση (α), όπως και η ανακατασκευή της απόκρισης. Το Σχήμα~\ref{fig:prob2b} δείχνει τα αντίστοιχα αποτελέσματα. -\InsertFigure{!ht}{1}{fig:prob2b}{../scripts/output/Prob2b_20s_Ts0.1.png}{ +\InsertFigure{!ht}{1.05}{fig:prob2b}{../scripts/output/Prob2b_20s_Ts0.1.png}{ Αποτελέσματα εκτίμησης παραμέτρων με χρήση μόνο του $q(t)$ και του $u(t)$. } @@ -248,21 +248,11 @@ \caption{Εκτίμηση με $\sigma = 0.0025$} \end{minipage} \end{figure} - \paragraph*{Παρατηρήσεις:} Για μικρό θόρυβο ($\sigma = 0.001$) η ακρίβεια παραμένει υψηλή (σφάλμα περίπου $10\%$). Όταν ο θόρυβος αυξάνεται ($\sigma = 0.0025$), οι εκτιμήσεις επιδεινώνονται σημαντικά, κυρίως για το $mL^2$. Το γεγονός αυτό οφείλεται στην αριθμητική παραγώγιση, η οποία είναι ιδιαίτερα ευαίσθητη στον θόρυβο. -\subsection{Υποερώτημα 3β: Επίδραση της Περιόδου Δειγματοληψίας $T_s$} -Στο υποερώτημα αυτό μελετάται η ακρίβεια των εκτιμήσεων σε συνάρτηση με την περίοδο δειγματοληψίας $T_s$. -Η προσομοίωση έγινε για διάρκεια $T = 20$ sec, ενώ τα δεδομένα δειγματοληττήθηκαν ξανά για διαφορετικές τιμές: -\[ - T_s \in \{0.01, 0.05, 0.1, 0.2, 0.5\} \text{ sec} -\] - -Η εκτίμηση έγινε με τον ίδιο τρόπο όπως στο Θέμα~2β. -Παρακάτω παρουσιάζονται τα σφάλματα εκτίμησης για κάθε παράμετρο. \textit{Το σχετικό σφάλμα υπολογίζεται ως:} \[ \text{Σφάλμα}_\text{σχετικό} = \left| \frac{\hat{\theta} - \theta_{\text{true}}}{\theta_{\text{true}}} \right| \times 100 @@ -278,6 +268,18 @@ \widehat{mL^2} \\\\ \hat{c} \\\\ \widehat{mgL} \end{bmatrix} \] + + +\subsection{Υποερώτημα 3β: Επίδραση της Περιόδου Δειγματοληψίας $T_s$} +Στο υποερώτημα αυτό μελετάται η ακρίβεια των εκτιμήσεων σε συνάρτηση με την περίοδο δειγματοληψίας $T_s$. +Η προσομοίωση έγινε για διάρκεια $T = 20$ sec, ενώ τα δεδομένα δειγματοληττήθηκαν ξανά για διαφορετικές τιμές: +\[ + T_s \in \{0.01, 0.05, 0.1, 0.2, 0.5\} \text{ sec} +\] + +Η εκτίμηση έγινε με τον ίδιο τρόπο όπως στο Θέμα~2β. +Παρακάτω παρουσιάζονται τα σφάλματα εκτίμησης για κάθε παράμετρο. +Το σχετικό σφάλμα υπολογίζεται όπως παραπάνω. \begin{table}[H] \centering \begin{tabular}{c|cc|cc|cc}