# Fig 5 Inverted Pendulum Free Body Diagram

## Fig 5 Inverted Pendulum Free Body Diagram

**inverted pendulum** is shown in **fig**.4.1 **Fig**.2.1 **Inverted Pendulum**-Cart System It is assumed here that **pendulum** rod is mass-less, and hinge is frictionless. The cart mass and the ball ... The **free body diagram** of cart system and **pendulum** is shown in **fig**.4.2 mass and **fig**.4.3. **Fig**.2.2 **Free Body Diagram** Of Cart **Fig**.2.3 **Free Body Diagram** Of **Pendulum**

of primary interest are the **pendulum** angle from the vertical µ and the cart position y. Note that the cart position is occasionally referred to as x. There is no appreciable difference between the two. Focusing on **Fig**. 1. **Inverted Pendulum Free Body Diagram**

**Modeling and Controller Design for an Inverted Pendulum** System ... assigning me the project titled “**Modeling and Controller Design for an Inverted Pendulum** System”. His supportive nature, continuous guidance and constructive ideas were really valuable ... 4.2.1 **Free body diagram** of the **Inverted Pendulum** system 12 **5**.1.1.1 Block **diagram** for ...

**Fig**. 2. **Free body diagram** of the **inverted pendulum** Summing the forces along the horizontal direction as shown in the FBD, following equation for N was obtained: N = mx&&+ ml θ&&cos θ−ml θ&2 sin θ (2) After substituting eqn. 2 into eqn. 1, the first equation of motion for the system was found as follows:

The **Inverted Pendulum** is one of the most important classical problems of Control Engineering. Broom Balancing (**Inverted Pendulum** on a cart) is a well known example of nonlinear, unstable control problem. This problem becomes further complicated when a flexible broom, in place of a rigid broom, is employed. Degree of complexity and

**Fig**.1. (a) **Inverted Pendulum** System (b) **Free Body Diagram** . T he system equations in state space form can be written as . ... **Fig**.**5**. Screen shot of LabVIEW Block **diagram** for pole placement of .

The cart with an **inverted pendulum**, is shownin **Fig**. 1. An impulse force F Newton is applied to the cartSomeassumptions are madefor modeling of an table 1. Table I.Assumption for **Inverted Pendulum** Symbol Parameter Value M Mass of the cart 0.**5** Kg ... **Fig**.1.**Free Body Diagram** of **Inverted Pendulum** ...

**Fig**.1.**Free Body Diagram** of **Inverted Pendulum**. From the transfer function above it can be seen that there is both a pole and a zero at the origins. These can be canceled and the transfer function becomes: Note that the forces can be sum in the vertical direction, = 3 + 2 2 + (14) From. but no useful information would be gained. Summing

simulation results of the **Inverted Pendulum** demonstrating the of the optimal LQR controller design. II. M. ODELLING OF THE **I NVERTED P ENDULUM** S YSTEM. Figure 1. Model and **free body diagram** of IP system . **Fig**. 1 shows that the general model of the **Inverted** Pendulumsystem [7]. The model consists of a **free** moving **pendulum** with the mass m

Verification: The study was verified through ‘root locus’ IV. Fabrication **diagram** drawn in MATLAB. **Fig**. 14 shows the root locus Initially the circuit was assembled on a ‘breadboard’ as it is **diagram** of the **inverted pendulum** robot. As is observed in easy to build and test.