Time - Optimal Control Problems for the Swing and the Ski 3 the 2 × 2
نویسنده
چکیده
This paper is concerned with a class of time-optimal control problems for the swing and the ski. We first consider the motion of a man standing on a swing. For simplicity, we neglect friction and air resistance and assume that the mass of the swinger is concentrated in his baricenter B. Let θ be the angle formed by the swing and the downward vertical direction and r the radius of oscillation, i.e. the distance between the baricenter B and the center of rotation O. Assuming that the mass is normalized to a unit, the corresponding Lagrangean function takes the form: L = 1 2 (ṙ + r θ̇) + g r cos(θ) (1.1)
منابع مشابه
MINIMUM TIME SWING UP AND STABILIZATION OF ROTARY INVERTED PENDULUM USING PULSE STEP CONTROL
This paper proposes an approach for the minimum time swing upof a rotary inverted pendulum. Our rotary inverted pendulum is supported bya pivot arm. The pivot arm rotates in a horizontal plane by means of a servomotor. The opposite end of the arm is instrumented with a joint whose axisis along the radial direction of the motor. A pendulum is suspended at thejoint. The task is to design a contro...
متن کاملApplication of Independent Joint Control Strategy for Discrete-Time Servo Control of Overhead Cranes
In this study, a new servo control system is presented for the overhead crane based on discrete-time state feedback approach. It provides both robust tracking and load swing suppression. Inspired from independent joint and computed torque control in robot manipulator field, a new model is derived in which the crane actuators are considered as the main plant. The crane nonlinearities are then tr...
متن کاملApproximate Pareto Optimal Solutions of Multi objective Optimal Control Problems by Evolutionary Algorithms
In this paper an approach based on evolutionary algorithms to find Pareto optimal pair of state and control for multi-objective optimal control problems (MOOCP)'s is introduced. In this approach, first a discretized form of the time-control space is considered and then, a piecewise linear control and a piecewise linear trajectory are obtained from the discretized time-control space using ...
متن کاملHaar Matrix Equations for Solving Time-Variant Linear-Quadratic Optimal Control Problems
In this paper, Haar wavelets are performed for solving continuous time-variant linear-quadratic optimal control problems. Firstly, using necessary conditions for optimality, the problem is changed into a two-boundary value problem (TBVP). Next, Haar wavelets are applied for converting the TBVP, as a system of differential equations, in to a system of matrix algebraic equations...
متن کاملSolution of Bang-Bang Optimal Control Problems by Using Bezier Polynomials
In this paper, a new numerical method is presented for solving the optimal control problems of Bang-Bang type with free or fixed terminal time. The method is based on Bezier polynomials which are presented in any interval as $[t_0,t_f]$. The problems are reduced to a constrained problems which can be solved by using Lagrangian method. The constraints of these problems are terminal state and con...
متن کامل