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b/src/pages/Week15.jsx @@ -4,14 +4,53 @@ import Navbar from '../Navbar'; import Anchors from '../assets/Anchors'; import Footer from '../assets/Footer'; const { Title, Paragraph } = Typography; +import { useEffect, useState } from "react"; +import ReactMarkdown from "react-markdown"; const Week15 = () => { const code1 = ` - + def nichols_plot_expr(system): + """Function to get the expression for Nichols plot.""" + s = system.var + w = Dummy('w', real=True) + sys_expr = system.to_expr() + H_jw = sys_expr.subs(s, I*w) + mag_expr = Abs(H_jw) + mag_dB_expr = 20*log(mag_expr, 10) + phase_expr = arg(H_jw) + phase_deg_expr = deg(phase_expr) + return mag_dB_expr, phase_deg_expr, w `; const code2 = ` - + def nichols_plot(system, initial_omega=0.01, final_omega=100, show=True, color='b', **kwargs): + _check_system(system) + magnitude_dB_expr, phase_deg_expr, w = nichols_plot_expr(system) + w_values = [(w, initial_omega, final_omega)] + p = plot_parametric( + (phase_deg_expr, magnitude_dB_expr), + *w_values, + show=False, + line_color=color, + title=f'Nichols Plot of {latex(system)}$', + xlabel='Phase [deg]', + ylabel='Magnitude [dB]', + size=(6,5), + kwargs=kwargs) + if show: + p.show() + return `; +const [readmeContent, setReadmeContent] = useState(""); +useEffect(() => { + // Fetch the raw content of the README.md file + fetch( + "https://raw.githubusercontent.com/abhiphile/GSoC-2024-SymPy-Final-Report/refs/heads/main/README.md" + ) + .then((response) => response.text()) + .then((data) => setReadmeContent(data)) + .catch((error) => console.error("Error fetching README:", error)); +}, []); + return ( <> @@ -22,41 +61,53 @@ const Week15 = () => {
- Week 15: Added Nichols plot to control. + Week 15: Added Nichols plot to control [Last Week] - This week, I focused on developing a Python function to generate Nyquist plots for + Due to recent travel and commitments related to college placements, I was unable to + complete all the expected work within the given timeframe. After discussing this + with my mentor, he suggested that I request an extension. I also feel that an + extension would allow me to complete the remaining work without added stress, so I + would like to request a 4-week extension to ensure I can deliver quality results. + + This week, I focused on developing a Python function to generate Nichols plot for continuous-time Single-Input Single-Output (SISO) Linear Time-Invariant (LTI) - systems. A Nyquist plot is a powerful tool used in control theory to assess the - stability of a system. + systems. A Nichols Chart is a graphical representation used to analyze and design + feedback control systems by depicting stability and frequency responses. The chart + works by transforming complex frequency responses into a simpler gain phase plane, + making it easier to analyze system behavior.
- The nyquist_plot function I developed takes a transfer function and generates the - Nyquist plot over a specified frequency range. I included customization options for - the plot's color, grid visibility, and whether or not to display the plot - immediately. + The nichols_plot function I developed takes a transfer function and + generates the plot over a specified frequency range.
One of the challenges I encountered was ensuring that the function could handle a wide range of systems and accurately plot the frequency response. By using the - plot_parametric function, I was able to plot the real and imaginary components of - the system's response, along with its mirror image, to create a comprehensive - Nyquist plot. -
- This function will be a useful tool for anyone working with control systems, as it - provides a visual representation of the system's stability across a range of - frequencies. -
- Next week, I plan to work on adding problems related to - StateSpace - and PIDController. - I've used the helper function _get_nyquist_expr() and used it to make - the nyquist plot. + plot_parametric function, I was able to plot phase and magnitude plot easily. Below + is my implemented code. + + nichols_plot_expr 
{code1}
- nyquist_plot function + nichols_plot 
{code2}
+ Nichols plot Example +
+ +
Fig - Nichols plot of 1.5 / (s^2 + 14s + 40.02)
+
+ The Final Report +
+ +
+ Pull Requests - - (Draft) Added nyquist plot to control plots. + + (Open) Added nichols_plot to control plots.