System Dynamics and Controls

EMB provides the building blocks to create simple and complex plants for dynamic system analysis, modeling, and control. We also offer fully assembled turnkey plants.

Example of plants include a DC motor with gears and an inertia wheel, flexible shaft, belt with spring (flexible spring), spring-mass-damper (linear system), rotary to linear motion with rack and pinion or belt, and MIMO plants with 2 actuators. 

Time to shake things up – literally! We're back with another classic: The Torsion Shaft Plant. Torsion shaft plants are staples in textbooks covering vibrations, dynamic systems, and control theory. Given the flexibility of our EMB system, the user can easily and quickly reconfigure the plant to add/remove weights, change shafts, and add disturbance. We offer pre-configured and assembled kits with 1, 2, and 3 Degrees of Freedom, supporting configurations such as rigid body, free-clamped, free-free. In this experiment, we vary the wheel’s inertia to observe its dynamic response. A sine sweep torque from 0 to 25 Hz is applied as the input. We performed 4 test runs with different inertia settings: - No weights added - 2 weights added - 4 weights added - 6 weights added FFT plots were generated for each run and compared. To learn more about our EMB system, visit: www.robots5.com #controlsystems #engineeringeducation #engineering #mechatronics #mechanicalengineering

We collaborated with our friend Logan Dihel on this project to develop an Energy Shaping controller to swing up a torque-limited pendulum. Logan has been working on tutorials for Drake, we highly recommend his tutorial series: https://www.youtube.com/@logandihel/videos We implemented the controller in #MATLAB and #Simulink from MathWorks and deployed to our EMB-DAQ1. The plant was created using our EMB system, with a motor and an encoder coupled by a timing belt and our pendulum arm attached to the encoder shaft. We saturate the actuator torque (EMB-AM4) to the following limits: - 0.01N-m - 0.02N-m - 0.04N-m - 0.08N-m Homoclinic orbits were generated for each case. When the pendulum is at the top, we switch to a PID controller. Due to the torque limit, this system becomes underactuated. Prof.Russ Tedrake from MIT has a complete class about this topic (he covers the torque-limited pendulum and energy shaping controller). More information here: https://underactuated.mit.edu/index.html To learn more about our EMB system, visit: www.robots5.com #robotics #controlsystems #engineeringeducation #engineering #mechatronics

Spring-mass-damper plants are found on virtually every textbook related to vibrations, dynamic systems and controls. This is our 3 Degrees of Freedom kit with one actuator and 3 moving masses, designed to explore free and forced vibration and control systems. Given the flexibility of our EMB system, the user can easily and quickly reconfigure the plant to add/remove springs, dashpots, and a disturbance module. To learn more, visit our website. #robotics #controlsystems #engineeringeducation #engineering #mechatronics

This is our 2 DOF Spring-Mass-Damper kit with one actuator and two moving carts, designed to explore free and forced vibration and control systems. Here we vary the mass, spring and damping coefficients to study the dynamic response to a force input. Given the flexibility of our EMB system (Electro-Mechanical Breadboard), the user can easily and quickly reconfigure the plant to add/remove carts, springs, dashpots, and a disturbance module. Spring-mass-damper plants are found on virtually every textbook related to vibrations, dynamic systems and controls. We offer pre-configured and assembled kits with 1, 2, and 3 Degrees of Freedom (DOF). The controller and data acquisition code was developed in #matlab and #simulink . Our products are designed and manufactured in the USA. To learn more, visit www.robots5.com #robotics #controlsystems #engineeringeducation #engineering #mechatronics

Example of a student project using our EMB System (Electro-Mechanical Breadboard). The controller and data acquisition code was developed in Python and pysimCoder. Hardware used: EMB-AM4 (Motor) EMB-LM1 (Linear slide with integrated encoder) EMB Rack and Pinion Attachment EMB Spring EMB-DAQ1 (Real-Time Target) Maxon ESCON (Amplifier in current control mode) Power Supply Software: pysimCoder NuttX Python RTScope #robotics #controlsystems #mechatronics #engineering #engineeringeducation #mechanicalengineering

Using the modularity of EMB, students can easily create an inverted pendulum plant. An EMB rotary encoder module is mounted to the top of an EMB linear slide that is driven by an EMB actuator module. The position of the cart is measured using the liner slide's internal linear encoder and the pendulum angle is measured with the rotary encoder. The Python code and pysimCoder diagram was based on the original pysimCoder examples from Professor Roberto Bucher (thank you!): https://lnkd.in/e4YMhwcf Python was used for modeling of the plant using Lagrange Method (SymPy) and the LQR balance controller with the Python Control Systems Library and custom functions from Prof.Bucher (available in pysimCoder). This Python script was linked to the pysimCoder diagram and real-time code was auto-generated for NuttX to run on the DAQ in real-time. Hardware: - EMB-AM4 (Motor) - EMB-LM1 (Linear Slide Block) - EMB-SM1 (Encoder) - EMB-MM2 (Bearing Block) - EMB Pendulum Attachment - EMB Rack and Pinion Attachment - EMB-DAQ2 (Real-Time Target) - Maxon ESCON (Amplifier) - Power Supply Software: - pysimCoder - NuttX - Python (system modeling and controller design) - PlotJuggler (real-time plotting via UDP from target) #robotics #controlsystems #mechatronics #engineering #engineeringeducation

Using the modularity of EMB, students can easily change the configuration and parameters of a physical plant, such as this spring-mass-damper system. The plant consists of an EMB linear slide driven by an EMB actuator module. The position of the cart is measured using the slide's internal encoder. The configuration of the plant is changed by adding mass, a spring, and a dashpot to the cart to study the robustness of the controller. A mathematical model of the plant without spring and dashpot was used for the controller design (Configuration #1). To perform parameter system identification and model validation, data from a step response was used. The controller was developed using Python and pysimCoder. The Python code and pysimCoder diagram were based on the original pysimCoder examples from Professor Roberto Bucher (thank you!). More information can be found here: https://github.com/robertobucher/pysimCoder-examples Hardware used: EMB-AM4 (Motor) EMB-LM1 (Linear slide with integrated encoder) EMB Rack and Pinion Attachment EMB Spring EMB Dashpot EMB mass blocks EMB-DAQ1 (Real-Time Target) Maxon ESCON (Amplifier) Power Supply Software: pysimCoder NuttX Python RTScope and PLotJuggler #robotics #controlsystems #mechatronics #engineering #engineeringeducation

Linear Pendulum Gantry Response to a 4N input force for 180ms. This exercise is used to find the system parameter values and to validate the mathematical model. Once the model is validated, a controller can be designed and implemented. An EMB rotary encoder measures the pendulum angle and an EMB linear encoder measures the cart position. An EMB actuator with a rack and pinion provides the input force to the cart. Data available for download (free) in our GitHub, for input forces of 2N, 3N, 4N, and 5N. Data includes time [s], force [N], motor current [A], cart position [m], and pendulum angle [rad]. Sampling time is 0.001s. Hardware: - EMB-AM4 - EMB-MM2 - EMB-LM1 - EMB-SM1 - EMB Pendulum attachment - EMB Rack attachment - EMB DAQ1 - Power supply - Maxon ESCON (in current mode) Software*: - pysimCoder - NuttX - RTScope * a special thank you to the open-source community for developing and maintaining these amazing tools! #robotics #controlsystems #engineeringeducation #engineering #mechatronics

Spring-mass-damper plants are found on virtually every textbook related to vibrations, dynamic systems and controls. This is our 3 Degrees of Freedom kit with one actuator and 3 moving masses, designed to explore free and forced vibration and control systems. Given the flexibility of our EMB system, the user can easily and quickly reconfigure the plant to add/remove springs, dashpots, and a disturbance module. To learn more, visit our website. #robotics #controlsystems #engineeringeducation #engineering #mechatronics

Short clip from Part 7 of our "EMB with pysimCoder" tutorial series. Using the modularity of EMB, students can create more complex plants such as a pendulum on a cart with a spring and damper. An EMB rotary encoder is used to measure the pendulum angle (green signal) and an EMB linear encoder reads the cart position (red signal). Hardware: - EMB-SM1 (Rotary Encoder) - EMB-LM1 (Linear Slide + Encoder) - EMB Pendulum - EMB-DAQ1 (Real-Time Target) - EMB Spring - EMB Damper Software: - pysimCoder - NuttX #robotics #mechanicalengineering #controlsystems #engineeringeducation #mechatronics

Using the modularity of EMB, students can study plants such as the Simple Pendulum. An EMB rotary encoder is used to measure the pendulum angle. Hardware: - EMB-SM1 (Encoder) - EMB Pendulum Attachment (just the pendulum) - EMB-DAQ1 (Real-Time Target) Software: - pysimCoder - NuttX - PlotJuggler #robotics #controlsystems #mechatronics #engineering #python

Time for a Classic: The Inverted Pendulum! Using the modularity of EMB, students can easily create an inverted pendulum plant. An EMB rotary encoder module is mounted to the top of an EMB linear slide that is driven by an EMB actuator module. The position of the cart is measured using the liner slide's internal linear encoder and the pendulum angle is measured with the rotary encoder. The Python code and pysimCoder diagram was based on the original pysimCoder examples from Professor Roberto Bucher (thank you!): https://github.com/robertobucher/pysimCoder-examples Python was used for modeling of the plant using Lagrange Method (SymPy) and the LQR balance controller with the Python Control Systems Library and custom functions from Prof.Bucher (available in pysimCoder). This Python script was linked to the pysimCoder diagram and real-time code was auto-generated for NuttX to run on the DAQ in real-time. Hardware: - EMB-AM4 (Motor) - EMB-LM1 (Linear Slide Block) - EMB-SM1 (Encoder) - EMB Pendulum Attachment - EMB Rack and Pinion Attachment - EMB-DAQ2 (Real-Time Target) - Maxon ESCON (Amplifier) - Power Supply Software: - pysimCoder - NuttX - Python (system modeling and controller design) - RTScope (real-time plotting) #robotics #controlsystems #mechatronics #engineering #robots5

Here is an example of how EMB (Electro-Mechanical Breadboard System) can be used to study spring-mass systems. We demonstrate 4 different spring rates (k) and compare the dynamic system response given a displacement input (same delta X for all runs). Hardware: - EMB-LM1 (Bearing block with linear encoder) - EMB Springs (4 rates) - EMB-DAQ1 (Real-Time Target) Software: - pysimCoder - NuttX - Inkscape (diagrams) - Excel+Python (plots) #robotics #engineeringeducation #controlsystems #mechatronics #engineering #robots5

Proper selection of gear ratio is a critical step when designing a dynamic system. Here is an example of how EMB (Electro-Mechanical Breadboard System) can be used to study inertia matching by gear ratio selection. We demonstrate 10 different gear ratio combinations and compare performance with the optimum gear ratio calculated via inertia matching. Hardware: - EMB-AM4 (Motor) - EMB-MM2 (Bearing Block) - EMB-SM1 (Encoder) - EMB Inertia Wheel - 0.5Mod and 0.8Mod gears - EMB-DAQ1 (Real-Time Target) - Maxon ESCON (Amplifier) - Power Supply Software: - pysimCoder - NuttX - Maple (Symbolic Mathematics and calculations) - Inkscape (diagrams) - Excel+Python (plots) Raw data available at: https://github.com/Robots5LLC #robotics #engineeringeducation #controlsystems #mechatronics #engineering #robots5

PID controllers have been around for about 100 years (since early 1920's, theoretical analysis and applications), and they are still the most common controllers used in industry. Here is an example of how EMB (Electro-Mechanical Breadboard System) can be used to study PID controllers. Hardware: - EMB-AM4 (Motor) - EMB-SM1 (Encoder) - EMB hub and linkage arm - MXL belt and pulleys - EMB-DAQ1 (Real-Time Target) - Maxon ESCON (Amplifier) - Power Supply Software: - pysimCoder - NuttX - Silicon Heaven (change values on the fly with real-time controller running) - RTScope (real-time plotting) #robotics #engineeringeducation #controlsystems #mechatronics #engineering #robots5

Do you want to have some fun with a cool dynamic systems challenge? Which option (1, 2, 3, 4, or 5) do you think will yield the highest angular acceleration on the second load? Here we derive the equation of motion and also run the experiment using our EMB products. Hardware: - EMB-AM4 (Motor) - EMB-MM2 (Bearing Block) - EMB-SM1 (Encoder) - EMB Inertia Wheels - 0.5Mod and 0.8Mod gears - EMB-DAQ1 (Real-Time Target) - Maxon ESCON (Amplifier) - Power Supply Software: - pysimCoder - NuttX - Maple (Symbolic Mathematics and calculations) - Inkscape (diagrams) - Excel+Python (plots) #mechanicalengineering #robotics #mechatronics #controlsystems #engineering

Example of how EMB (Electro-Mechanical Breadboard System) can be used to study the effect of increasing the inertia of the load. The results of this experiment can be used to characterize the motor and validate the mathematical model. Here we demonstrate 3 different plant variations: - Motor with no Inertia Wheel - Motor with 1 Inertia Wheel - Motor with 2 Inertia Wheels Hardware: - EMB-AM4 (Motor) - EMB-MM2 (Bearing Block) - EMB-SM1 (Encoder) - EMB Inertia Wheel - EMB-DAQ1 (DAQ Target to run real-time code) - Maxon ESCON (Amplifier) - Rigol Power Supply Software: - pysimCoder - NuttX - Inkscape (diagrams) - Excel+Python (plots) Raw data available at: https://github.com/Robots5LLC #robotics #engineeringeducation #controlsystems #robots5

Spring-Mass-Damper plants are found on virtually every textbook related to Vibrations, Dynamic Systems and Controls. Here we demonstrate 4 different plant variations, using EMB: - Spring, mass, no damper - Spring, mass, with damper - Spring, double mass, no damper - Spring, double mass, with damper Notes: - Spring: the same spring is used for all runs, with a spring rate of 2.59 lbs/in (453 N/m). - Carriage mass: 550g - Double Mass: 570g (in addition to carriage mass) - Damper: the damper and its coefficient (adjustable) is also the same between the runs with damper. - Sampling time: 0.001s #robotics #engineeringeducation #controlsystems #robots5

The EMB-LM1 is the new linear module in our line of products. With a low friction ball slide, a high resolution linear encoder, and dovetails that easily interface with other EMB modules, the EMB-LM1 is ideal for plants that have translational components, including spring-mass-damper, rack and pinion, and belt driven linear slide. If your students are looking for a challenge, multiple EMB-LM1 modules can be connected in series or parallel to create higher order dynamic systems. For more information, visit: www.robots5.com #robotics #controlsystems #engineeringeducation #robots5

EMB can be used to develop more complex plants, such as multiple input, multiple output systems. With this example, we explore disturbance rejection of a MIMO plant, using different controller designs. #engineering #controlsystems #robotics #mechatronics #robots5

Here we vary the input sine wave frequency and observe the system response. Frequency of input sine wave varies from 0Hz to 30Hz. Plant is a motor and encoder with a timing belt, assembled with EMB modules. Note the response amplitude and phase change. Performance can be improved with optimum controller gains. Components used: - EMB-AM4 (Motor) - EMB-SM1 (Encoder) - EMB-DAQ1 (Controller and real-time target) - EMB-IM1 (Interface module) - Copley amplifier - Power Supply - Estop - Linux desktop - pysimCoder (software used to create the code and generate real-time code to target deployment) - RTScope (real-time plotting data) - Silicon Heaven (change values while code is running on the target) #engineering #mechatronics #robotics #engineeringeducation #robots5

Example of how EMB (Electro-Mechanical Breadboard System) can be used to study the effect of a flexible shaft in control systems. The students develop a controller using encoder "A" and encoder "B" for feedback, to meet a set of performance requirements. #mechanicalengineering #robotics #controlsystems #controlsengineering #engineeringeducation

Flexible Link Experiment, where the students develop an LQR controller to minimize link tip deflection. An encoder connected to the motor and a load cell connected to the flexible link are used for feedback. At Robots5, we encourage the students to 3D print, machine, and laser cut components to integrate with EMB. Here, 3D printed parts were used as part of this experiment. #mechanicalengineering #robotics #controlsystems #controlsengineering #engineeringeducation

Quick example of pysimCoder being used to control a servomotor plant. #education #robotics #controlsystems

Example of how EMB (Electro-Mechanical Breadboard System) can be used to study the open loop response of a DC motor. Students also explore the effect of increasing the inertia of the load. The results of this experiment are used to characterize the motor and validate the mathematical model.

Example of how EMB (Electro-Mechanical Breadboard System) can be used to study the effect of friction in rotary systems. The results of this experiment are used to characterize the friction parameters and validate the mathematical model. #mechanicalengineering #robotics #controlsystems #controlsengineering #engineeringeducation

The EMB - SC Kit was designed specifically for servo control studies. The kit has an actuator (DC motor) and a feedback device (either an encoder or a potentiometer). A range of experiments such as open and closed loop control, plant characterization and analysis, position and speed control. An additional sensor can be used for user set point, to explore concepts of "drive by wire". #controlsystems #engineeringeducation #mechanicalengineering

pysimCoder, created by Professor Roberto Bucher, is our preferred tool for dynamic systems modeling, simulation, control, and real-time code generation. The user can link Python Scripts to the block diagram, making this an extremely powerful application. After the code is generated, it can be deployed to a target, including PC, STM32 board, Raspberry Pi, or NuttX RTOS! Once the code is running in the target, Silicon-Heaven can be used to change parameters such as controller gains, setpoint, limits. For more information about pysimCoder, Silicon-Heaven, and NuttX, check out: https://github.com/robertobucher/pysimCoder https://github.com/silicon-heaven https://github.com/apache/incubator-nuttx Thank you Professor Roberto and everyone involved!

Feedback control system instability slow motion.