Because the way theta is defined (with respect to the vertical) it increases in the 'negative' (clockwise) direction. If they defined theta with respect to the horizontal then you'd be correct.Arslan said:i have problem with the equation encircled in red in the figure. I(theeta)''=sum of all torqes acting on the body. but they are taking torques in the negative direction why.
It should be -VLsin+HLcos=I(theeta)''
All true, but irrelevant. It's just a matter of sign convention. Since theta is defined in the clockwise direction, torques in the clockwise direction will be positive.Arslan said:but the body is rotating along its center of gravity. If the force is applied on cart, the cart will move in the forward direction and transfer the force to the rod in the direction of red arrow, and the body will rotate along its center of gravity. So body is rotating in counter clockwise direction.
The inverted pendulum problem is a classic control theory problem that involves balancing an upright pendulum on a moving base. The goal is to design a control system that can keep the pendulum balanced despite the constant disturbance from the base.
The inverted pendulum problem is important because it serves as a benchmark for testing and developing control theories and algorithms. It also has practical applications in areas such as robotics, aerospace, and transportation.
The main challenges in solving the inverted pendulum problem include the highly nonlinear dynamics of the system, the constant disturbance from the base, and the limited information available for feedback control.
The inverted pendulum problem is typically solved using various control strategies, such as proportional-integral-derivative (PID) control, model predictive control, and reinforcement learning. These strategies rely on mathematical models and algorithms to calculate the appropriate control actions to keep the pendulum balanced.
The inverted pendulum problem has several real-world applications, including balancing robots, self-balancing scooters, and aircraft control systems. It can also be used to study and improve human balance and stability control, as well as for developing advanced control techniques for complex systems.