CONTROL AND DESIGN OF AN INVERTED PENDULUM ON A CART
Controlling of an Inverted Pendulum is a classical control problem and widely referred in the literature. The system is inherently an unstable nonlinear system. The aim of this project is to design a linear controller for stabilizing the inverted pendulum at its unstable equilibrium point. This work
2025-06-28 16:30:55 - Adil Khan
CONTROL AND DESIGN OF AN INVERTED PENDULUM ON A CART
Project Area of Specialization RoboticsProject SummaryControlling of an Inverted Pendulum is a classical control problem and widely referred in the literature. The system is inherently an unstable nonlinear system. The aim of this project is to design a linear controller for stabilizing the inverted pendulum at its unstable equilibrium point. This work shall include detailed mathematical modeling and analysis of this physical system and shall propose an efficient design for ensuring stabilizing control. The model with and without controller will be analyzed theoretically and validated using simulations. A complete indigenously developed physical system (Testbed) shall then be implemented using the proposed design to ensure stability of the system. Various control strategies, including the PID based controllers and optimal controllers like the Linear Quadratic Regulator (LQR), shall be tested and implemented on the hardware. Artificial Intelligence based control techniques can also be tested later on the system to stabilize the inherently unstable system. National Instruments' MyRIO shall be used to implement the controller and for interfacing the hardware with the software i.e. LabVIEW. This work shall be used as a testbed for analyzing and validating various linear and even nonlinear control strategies, both at undergraduate and graduate level. The proposed testbed can also be converted into a full scale system as a commercial product for any robotics/control industry or academia.
Project Objectives- Indigenous Development of testbed that can be used for analyzing classical and modern control strategies, including PID, LQR (Optimal Control), State Feedback Control, Output Feedback Control and Sliding Mode Control, for a class of nonlinear benchmark system, 'The Inverted Pendulum'.
- Stabilizing the system at its unstable equilibrium point after analyzing the unstable system dynamics.
- Mathematical Modeling of the entire system using appraoches like the state space.
- Validation of the Mathematical Model on Simulation (Matlab).
- Design of various Stabilizing Controllers and its validation using Simulation (Matlab).
- Practical Implementation of the Entire System using National Instruments' MyRIO and LabVIEW.
The inverted pendulum is a classical control problem, often encountered as an application of robotics/mechatronics, which involves developing a system to balance a pendulum at its unstable equilibrium point. To study this problem, this project shall incorporate the following implementation method.
Step #1 Mathematical Modelling of the System
The entire system shall first be modeled using standard engineering mechanics' concepts to properly analyze the mechanical system. Torque and force balancing equations shall be used to obtain the dynamic model of the system. Since the control strategies to be used in this project are based on state space design, the model shall be converted into state space representation before the control is designed. The model shall also be analyzed using MATLAB to observe the unstable dynamics associated with the system.
Step # 2-Design of Testbed
The mechanical design includes building a track/railing, a cart, a pendulum, and a drive mechanism along with a DC motor. The track, cart, and pendulum shall be developed using primarily aluminum and wood. The parameters for the design have been selected.
Step # 3 The Sensory and Feedback Network.
Basically the angle of the pendulum shall be used as the primary feedback parameter along with the angular velocity. Apart from that, the translational motion of the cart shall also be monitored and incorporated as desin input parameter for the optimal control problem (LQR Control). The feedback network shall consist of rotary encoders to measure the angle of the pendulum and the horizontal displacement of the cart. A drive mechanism (DC motor) shall take corrective measures based on the received feedback from the the sensors. The drive mechanism is a DC motor, which the cart connects to the position of the cart. The control circuitry for a DC motor is typically an H-bridge which controls the direction of current across the motor based on the directional signal. For interfacing hardware with software (LabVEIW), MyRio shall be used.
STEP # 4- Controller Design and Implementation
Two controler design strategies shall be proposed in this project. The first design, PID controller, shall incorporate only the angle measurements as design parameter and shall be able to stabilize the system at its unstable system.
The second design, LQR Controller. will be an optimal control solution that shall also cater for the applied input along with the stability problem. This approach is expected to yield a more advanced design.
Both the controllers shall be implemented using myRIO due to its advanced features and specifications over other standard hardwares like the Arduino boards.
Benefits of the Project- Testbed for analyzing and validating various linear and even nonlinear control strategies, both at undergraduate and graduate level.
- The proposed testbed can also be converted into a full scale system as a commercial product for any robotics/control industry or academia.
- A cost effective and efficent setup for any control based course/lab offered in various engineering programs including Electrical, Electronics and Mechanical Engineering.
- The concepts validated through this test beds can be applied on physical control systems including those in aeronautical systems, other military applications including missile systems and naval weapon systems as well, thus contributing in national indigenous development.
- An indigenously developed complete solution for stabilizing the nonlinear benchmark system (The Inverted Pendulum).
- A mechanical platform with railing, cart and a suspended pendulum as the nonlinear system with all specifications.
- State Space Based Model of the Hardware to be made available on Paper and on MATLAB.
- PID controller (Proposed Design # 1) able to stabilize the inherently unstable system designed on Paper and on MATLAB,
- Optimal (LQR) controller (Proposed Design # 2) able to stabilize the inherently unstable system designed on Paper and om MATLAB,
- Fully working sensory and Feedback network incorporating encoders for angle and position measurements, circuitry for driving DC motor.
- Proposed Design # 1 and Proposed Design # 2 implemented on the hardware using National instruments' MyRIO and interfaced using LabVIEW.
- Complete and detailed paperwork with a report and presentation.
| Item Name | Type | No. of Units | Per Unit Cost (in Rs) | Total (in Rs) |
|---|---|---|---|---|
| Total in (Rs) | 67500 | |||
| Mechanical Platform (Railing, Cart and Pendulum Rod) | Equipment | 1 | 25000 | 25000 |
| Motors | Equipment | 2 | 3000 | 6000 |
| Incremental Encoder | Equipment | 1 | 6000 | 6000 |
| Absolute rotary Encoder | Equipment | 1 | 22000 | 22000 |
| Drive Circuitry (H-Bridge and amplifier circuit) | Equipment | 1 | 6000 | 6000 |
| Report Printing/Binding | Miscellaneous | 5 | 500 | 2500 |