plotting_with_matlab.mlx Gives a rapid overview of the vector notation used to support line plots and the plot command.
ODEs_with_matlab.mlx Shows how MATLAB can be used to give both analytic and numerical solutions of ODEs. Includes examples of how to plot the solutions.
firstordermodels_in_matlab.mlx Shows how to create models in MATLAB to represent systems.
firstordermodels_responses_analysis_and_feedback.mlx A holistic storyline script which begins from modelling 1st order models in time constant form, identifying parameters from data and then moves on to analysis and design of proportional and PI feedback compensators.
secondordermodels_in_matlab.mlx Shows how to create models in MATLAB to represent systems
secondordermodels_and_under-damping.mlx Illustrates under-damped 2nd order behaviours and the impact of the damping ratio and natural frequency. Uses Laplace based models.
laplace_transforms_with_matlab.mlx Shows how to find the Laplace transform of a time domain signal and the inverse Laplace of a transform. Focuses on analytic solutions. Files below this largely focus on numerical solutions.
partial_fractions_with_matlab.mlx Partial fractions are a core part of inverse Laplace and understanding behaviours. This file shows how MATLAB can support such computations where required.
transferfunctions_and_poles.mlx Shows how to create a transfer function in MATLAB and also to find its poles and zeros which in turn characterise the expected behaviours.
transferfunctions_and_behaviours.mlx Shows how to create a transfer function in MATLAB and also to characterise and plot the expected behaviours.
step_responses_with_matlab.mlx Step responses are a cornerstone of system behaviours and supported by the MATLAB step.m command. This file illustrates several different ways step.m can be used.
closedloop_transferfunctions_with_feedback.mlx Introduces the feedback.m file for computing closed-loop transfer functions.
closed_vs_openloop_overlay.mlx Demonstrates code for overlaying the closed-loop responses with different choices of compensator so you can compare and contrast different designs. Allows 3 different compensators but uses transparent (inefficient) coding for simplicity so users can follow the core steps.
closed_loop_compare_multiple_compensators.mlx This file provides more efficient coding for comparing numerous compensators on the same system. Allows any number of compensators with minimal changes in the code required (just enter the required system definitions).
closedloop_offset_and_poles.mlx Focuses specifically on how to compute the closed-loop poles and offset (percentage).
PID_tuning_methods.mlx Introduces a number of popular rules for tuning PID compensators.
freq_response_with_matlab.mlx Introduces users to the concept of frequency response and how the gain and phase might be computed from both time domain responses and with complex algebra (i.e. bode.m). [Needs the file ds2nfu.m to support some internal illustrations.]
bode_asymptotes.mlx While modern computing means there is less need to sketch Bode diagrams by hand, some basic insight and understanding into the basic shapes is useful in analysis and design. This file produces asymptote plots to aid such insight.
proportional_design_with_bode.mlx A simple proportional design is often based on a phase margin criteria. This livescript explains and illustrates the key steps.
lag_design_with_bode.mlx This file explains the core steps behind a mechanistic lag design (PM and low freq. gain criteria) and illustrates with examples.
lead_design_with_bode.mlx This file explains the core steps behind a mechanistic lead design (PM and bandwidth criteria) and illustrates with examples.
lead_lag_design_with_bode.mlx This file explains the core steps behind a mechanistic lead-lag design (PM, low freq. gain and bandwidth criteria) and illustrates with examples. Also compares with a lag design and a lead design.
PID_Cont_Controller_Design_with_Pole_Cancellation.m This file explains the core steps behind a mechanistic PID design using a pole cancellation technique and exploiting frequency response methods.
delays_and_bode.mlx Real systems are often subject to small delays, perhaps due to actuator placement or measurement issues. This file allows users to explore the impact of delays on expected closed-loop performance and indeed to consider how a system re-design of the compensator may be considered.