Question

Problem 6 State space representation of motor - driven cart with inverted pendulum You are given that the cart carrying the inverted pendulum shown in the figure below is driven by an electric motor powering one pair of wheels so that the whole cart, pendulum and all, becomes the load on the motor. z is the cart position, M is its mass, θ is the pendulum angle with respect to the vertical, I its length, and m its mass. The linearized equations of motion for the system, for small changes of about zero, are Mr2R MRrla where k is the motor torque (or back emf) constant, R is the armature resistance, r is the ratio relating motor torque T to the force fapplied to the cart (T rf), and ea is the armature voltage. You are given the following parameter values ,n : 0.1 Kg M-1.0kg 1-1.0 m g-9.8 m/sec k-1 V.sec/rad- 1 N.m/V R-1000.02 m a) Let the state vector, input, and output vector be defined by Find the matrices A, B, C, D for the state space realization. Use numerical values for the matrix elements b) Draw a simulation diagram for the system with the states as the integrator outputs. Use numerical values for the gains in the simulation diagram

Answer 1