Problem 6 State space representation of motor - driven cart with inverted pendulum You are given...
Problem 1 The linearized dynamic model of a inverted pendulum are given by where a i,l' with ri=() pendulum angle r pendulum angular velocity ue voltage on d e motor driving the pendulum 3 2 A Tull state teedback control law is to be designed that plases the closed loop poles at 1:313 Problem 2 is made that the gains determined in Problem I are linear-quadratic optimal for the weighting Verify or refute this claim
Problem 1 The linearized dynamic...
This assignment is for my Engr dynamics systems class.
Consider the electromechanical dynamic system shown in Figure 1(a). It consists of a cart of mass m moving without slipping on a linear ground track. The cart is equipped with an armature-controlled DC motor, which is coupled to a rack and pinion mechanism to convert the rotational motion to translation and to create the driving force for the system. Figure 1(b) shows the simplified equivalent electric circuit and the mechanical model...
Problem 3 (70 pts): Consider the mechanical system in Figure , the so-called "cart pendulum" system. The cart has a moving mass M, and is connected to a linear motor via a flexible coupling with stiffness K and damping B. An inverted pendulum of length1, negligible inertia and mass m is attached to the cart via a rotary actuator. If the pendulum damping coefficient is b, the linear actuator force is F and the rotary actuator torque is t 1)...
Problem 1 An inverted pendulum driven by a d-c motor is governed by the following differential and algcbraic equa tions: (a) Determine the transfer function of the process. (b) It is proposed to control the process using "proportional control": where yr is a constant reference value. Determine the value Kmir for which the gain K must exceed in order that the closed-loop system be stable. (c) Determine the value of K for which the magnitude of the error is less...