A simple interface emphasis the core role of the time constant and gain parameters in the step response behaviour and convergence.

Allows the user to vary the model parameters and initial condition and visualise the core invariance aspects in the response and how these relate to time constant and gain. User simply moves the sliders and the figure updates.

A simple interface to practice estimation of time constant and gain from a step response for a 1st order model. The app supports students in being able to make quick and accurate estimates of the time constant and gain and to check the accuracy of their estimates against the true answers. 

The figure keeps track of multiple attempts so students can iterate intelligently and thus improve their understanding.

How quickly and where does the level in a tank settle given a fixed in flow, and variable area/outlet resistance? The figure gives a visualisation of the tank attributes so users can: i) manually (through yellow sliders) change the area/outlet resistance and in-flow; ii) modify the environment/disturbances (green sliders) and iii) simulate to see the actual behaviour, time constant and gain.

The lower right figure store previous simulations so the user can observe trends and understand design principles. Animation effects in the top figure bring some life and visualisation to the app. The bottom left figure focuses on an analysis of the time constant and gain.

Investigate the depth level control of a tank with a PI design,  Use sliders to select PI values and the dimensions of the tank. 

Uncertainty is included in two forms:

1. A small disturbance in-flow (either added throughout ir introduced mid-simulation).

2. A partial blockage of the outlet pipe (either continuous, or considered as an impact on a steady-state start point).

The lower figures store previous simulations so the user can observe trends and understand design principles. Animation effects in the top figure also bring some life and visualisation to the app.

This file takes a user through the entire process of modelling, analysing, controller design and final evaluation, for a tank level system, in the presence of multiple forms of uncertainty. Different tabs move the user along the storyline. The first tab explores open-loop behaviour and the impact of flow disturbances and blockages to the outlet pipe. The second tab focuses on modelling in time constant form. The third tab covers manual control subject to uncertainty. The fourth tab introduces PI design and the fith tab is an opportunity to evaluate the final PI design, subject to more varied uncertainty, so including sensor delays and measurement noise.         

For tabs 1, 3 and 4, the top right figure store previous simulations so the user can observe trends and understand design principles; use refresh if  this is unhelpful. The bottom right figure forms a different role in each tab so is automatically refreshed for each simulation. Animation effects in the top figure also bring some life and visualisation to the app.

We consider a heat exchanger with inlet and outlet pipes and a constant flow rate. The inlet temperature is not the same as the outlet temperature due to supplied heating and thus, assuming good mixing, the inlet flow will gradually change temperature, represented by colour, in the tank. In practice there may also be a disturbances to the inlet temperature and flow rate, as well as changes in tank volume and heating; users can investigate the associated behaviours with this app. 

This app allows users to investigate the dependence of a car speed behaviour on simple parameters such as car mass, friction, engine power, road slope and wind.

It also has a figure to emphasise the computation of an equivalent first order model in time constant form.

The lower figures store previous simulations so the user can observe trends and understand design principles. Animation effects in the top figure also bring some life and visualisation to the app.

We consider a car can be represented as a simple mass-damper model, the damping representing friction which is assumed proportional to velocity and throttle position gives effective force on the road. We wish to control the speed of the car and also, subject to wind and slope variations so a PI compensator is adopted.

This app allows the user to explore the impact on closed-loop behaviour of variations in the car and PI parameters and disturbances.

Allows the user to investigate the behaviour of a thermal system, here represented by a simple house heating model. The user can change the size of the house (thermal capacity), wall thickness/insulation (heat loss), heat supply, external temperature and initial condition. 

This app allows the user to explore/overlay the impact of different choices on the behaviour. Red represents hot and blue represents cold.

This file takes a user through the entire process of modelling, analysing, controller design and final evaluation, for a thermal system, in the presence of multiple forms of uncertainty. Different tabs move the user along the storyline. The first tab explores open-loop behaviour and the impact of external temperature disturbances and wind chill. The second tab focuses on modelling in time constant form. The third tab covers manual control subject to uncertainty. The fourth tab introduces PI design and the fith tab is an opportunity to evaluate both the final PI design and on-off control, subject to more varied uncertainty, so including sensor delays and measurement noise.     

Red represents hot and blue represents cold and green arrows represent the wind chill.  For tabs 1, 3 and 4, the top right figure store previous simulations so the user can observe trends and understand design principles.

We consider a DC servo driving a simple passenger on a seat along a track. This app allows the user to investigate both open-and closed-loop behaviour. 

• How does open-loop behaviour change with different loads, frictions, gear ratios and so forth?  

• Can we design an effective PI compensator for either or both speed and position control?

• Users can also add an additional transient friction as a realistic disturbance type.

Allows the user to investigate the behaviour of 2nd order mass-spring-damper systems through the example of the suspension unit under and landing aircraft. 

This app allows the user to explore/overlay the impact on landing behaviour and passenger comfort (oscillation and acceleration) of variations in the suspension parameters and plane mass. 

Allows the user to investigate the impact of real environmental issues on the control of an inverted pendulum. For example:

1. Lag in decision making/actuation associated to a DC servo driving cart motion.

2. Lag in decision making with human control.

3. The impact of delay associated to human decision making.

This app allows the user to explore/overlay the impact on closed-loop behaviour of variations in the the choices above.

Allows the user to investigate the impact of pole positions on linear system behaviour. Allows real, complex and unstable poles. Three different tabs:

1. The first has fixed but illustrative systems.

2. The second allows the user to enter transfer function coefficients directly.

3. The third generates random examples with specified characteristics.

The user can also use the mouse to 'move/change' pole and  zero positions using the bottom right hand picture.

Predator prey models are an example of a non-linear ystem. Non-linear systems have far more complex and sometimes complicated behaviour compared to linear systems and at times appear to behave in a somewhat chaotic fashion.  This scenario also implicitly contains feedback between the different model states. The scenarios and choices in the app allow for relatively simple changes in the parameters, but these are enough for users to observe and understand the associated complexity of the behaviours. 

Allows the user to practice doing some PI designs on a range of simple systems with fixed dynamics. The closed-loop has a simple standard block diagram as shown, with C(s) the compensator and G(s) the system.

The custom tab allows the user to enter a system of their own choice.

Allows the user to practice using some standard PID tuning methods on a range of simple systems with fixed dynamics. Inlcudes Ziegler Nichols, Cohen Coon, Amigo, One third, Skogestad and Lambda tuning. More detailed technical and analytical background is provided  in the partner livescript file pidtuningrules_manual.mlx and pid_tuning_methods.mlx. The latter file also includes some simple MATLAB code snippets than can be used for equivalent analysis.

This is a simple interface to understand the concept of frequency response in a time domain scenario.  Users can excite a variety of lienar systems with a sinuosidal input and view the system responses. The figures are presented in such a way that users can infer the implied gain and phase shifts of the output relative to the input. Numerical calculations are also provided. More detailed technical and analytical background is provided  in the partner livescript file frequency_response_time_behaviour_manual.mlx. This file also includes some simple MATLAB code snippets than can be used for equivalent analysis.

This resource provides an interactive app file (MATLAB virtual laboratory) which demonstrates how to perform a simple lead compensator feedback design using Bode diagrams with a phase margin and bandwidth criteria. The app includes a number of pre-coded examples and allows the user to investigate both how to meet the requirements and the impact of this on closed-loop behaviour. The manual and app also give guidance on a mechanistic design to achieve the specified criteria. For completeness the behaviour with the lag compensator is compared with a simple gain design, so the differences can be evaluated.

This resource provides an interactive app file (MATLAB virtual laboratory) which demonstrates how to perform a simple lead-lag compensator feedback design using Bode diagrams with a phase margin, bandwidth and low frequency gain criteria. The app includes a number of pre-coded examples and allows the user to investigate both how to meet the requirements and the impact of this on closed-loop behaviour. The manual and app also give guidance on a mechanistic design to achieve the specified criteria. The low frequency gain criteria takes two alternative forms depending upon whether the system includes and integrator or not. For completeness the behaviour with the lead-lag compensator is compared with a simple gain design and a lead only design, so the differences can be evaluated.

The apps above establish that proportional, lag, lead and lead-lag design can be tied explicitly to the design criteria of phase margin, bandwidth and offset. Consequently, fix the criteria and the design is also fixed. This app allows users to compare and contrast the behaviour and performance of different compensators arising from such a criteria based design approach and indeed, to observe that criteria are not always achievable.

Allows the user to investigate the efficacy of simple lead compensation for controlling the roll angle of a simple aircraft.

The app shows the Bode diagrams with core attributes of the compensator and compensated cross-over frequencies/margins to help the user make sensible choices. 

The bottom figure will store previous designs to allow a compare and contrast investigation.

Students can investigate parallel  (closed switch) and series (open switch) arrangements; the switch indicates the arrangement but the figure shows data for both regardless. 

When the resistances R2 and/or R3 are changed the figure adds a new point so that trends can be observed.

This app assumes a stable 2nd order system with a constant numerator and illustrates the conventional analysis of overshoot, oscillation and 1st peak overshoot time (half period).  Users can use random examples or enter the denominator coefficients directly to investigate the impact of varying damping and frequency.

Allows students to randomly generate transfer functions of different orders, with or without complex poles and with or without unstable poles. Alternatively, enter the numerator and denominator parameters directly into the boxes. The right hand figure shows the pole and zero positions. "Test my results" shows the unit step response.

[Warning: random generation may include a pole on the origin which results in a step response with a ramp.]

House is treated as a  thermal capacity with heat losses depending on insulation. As users change these two properties and update figure, the house changes to visualise what has happened. Expectations on the corresponding behaviour can then be validated through "test my results".

The 2nd app is similar but adds some animations to help with the visualisation, overlays plots so users can plan investigations of trends and also includes a greater variety of possible parameters. The thickness of the walls links to insulation and the redness to hotness.

A  video giving some background and illustrations of usage is available here.

Users can create random parameter values through 'new example' or enter values directly in the brown boxes. Update figure gives a visualisation and "test my results" computes the core 2nd order dynamic values of interest (damping ratio, gain, time constant) so users can compare with their own computations.