The electromechanical system shown in Fig. The system consists in part of a parallel plate capacitor connected into an electric circuit. Capacitor plate a is rigidly fastened to the microphone frame. Sound waves pass through the mouthpiece and exert a force fe t on plate b, which has mass M and is connected to the frame by a set of springs and dampers. It is acceptable to leave in nonlinear form.
A very typical problem of electromechanical position control is an electric motor driving a load that has one dominant vibration mode. The problem arises in computer-disk-head control, reel-to-reel tape drives, and many other applications. A schematic diagram is sketched in Fig.
The motor has an electrical constant Ke , a torque constant Kt , an armature inductance La , and a resistance Ra. The rotor has an inertia J1 and a viscous friction B. The load has an inertia J2. The two inertias are connected by a shaft with a spring constant k and an equivalent viscous damping b.
Write the equations of motion. For the robot in Fig. Determine the dynamic equations relating the speed of the robot with respect to the torque command of the servo. Your equations will require certain quantities, e. Assume you have access to whatever you need. That is, a system where the torque is applied by a motor on a gear that is simply accelerating an attached gear, like the picture in Fig.
In order to multiply the torque by a factor of 2, the motor must have a gear that is half the size of the gear attached to the wheel, i. If the wheel was not attached to the robot, Eq. So that means we need to add the rotational inertia of the two other wheels and the inertia due to the translation of the cart plus the center of mass of the 3 wheels.
The acceleration of all these quantities are directly related through kinematics because of the nonslip assumption. That means, if we neglect the translation inertia of the system, the equation becomes. When you apply a torque to a drive wheel, that torque partly provides an angular accelation of the wheel and the remainder is tranferred to the contact point as a friction force that accelerates the mass of the vehicle. That friction force is. So the end result is:. Using Fig. Solution: Equation 2.
Adding the spring torque to Eq. A precision-table leveling scheme shown in Fig. The system input is vi and the system output is d: Type 1 Type 2 Type 1.
We can expect the hotest rooms on the outside and the corners hotest of all, but solving the equations would con…rm this intuitive result. Assume that Eq. The square root functions need to be linearized about the nominal heights. Instead, there will be a constant term increasing h2 : Thus the standard transfer function will not result. The equations for heating a house are given by Eqs. It is measured that, with the outside temperature at 32 o F and the house at 60 o F , the furnace raises the temperature 2 o F in 6 minutes 0.
What are the values of C and R for the house? In both cases, it is a …rst order system and thus the solutions involve exponentials in time. The approximate answer can be obtained by simply. Authors: Gene F.. For senior-level or first-year graduate-level courses in control analysis and design, and related courses within engineering, science, and management Feedback Control of Dynamic Systems covers the material that every engineer, and most scientists and prospective managers, needs to know about feedback control-including concepts like stability, tracking, and robustness.
Each chapter. Da Powell, Abbas Emami-Naeini. The emphasis is on the design of digital controls that achieve good dynamic response and small errors Two new chapters have been added to the third version offering an overview of feedback control programs and a summary of digital control systems. Firstly, based on the MSFs method, a sufficient condition for the existence of the passivity of the underlying system is established in terms of linear matrix inequalities LMIs.
Written for undergraduate and graduate-level courses in control theory. Abstract: Introduction to the state-space approach to control system analysis and control synthesis. Feedback Control of Dynamic Systems. Feedback Control of Dynamic Systems, 3e Scripts 1. From Eq. We can see that the pole is at the left side of the zero, which means a lead compensator.
We can see that the pole is at the right side of the zero, which means a lag compensator. There are a couple of methods to …nd the transfer function from Vin to Vout with set of equations but for this problem, we will directly solve for the values we want along with the Laplace Transform. From the …rst three equations, slove for V1; V2. Vin R1. Find the equations and transfer function for the biquad circuit of Fig.
The torque constant of a motor is the ratio of torque to current and is often given in ounce-inches per ampere. The electric constant of a motor is the ratio of back emf to speed and is often given in volts per rpm. In consistent units the two constants are the same for a given motor. What is its torque constant in ounce-inches per ampere?
Some remarks on non SI units. Actuall, the ounce is a unit of mass, but like pounds, it is commonly used as a unit of force.
If we translate it as force,. The electromechanical system shown in Fig. The system consists in part of a parallel plate capacitor connected into an electric circuit. Capacitor plate a is rigidly fastened to the microphone frame. Sound waves pass through the mouthpiece and exert a force fs t on plate b, which has mass M and is connected to the frame by a set of springs and dampers. It is acceptable to leave in nonlinear form. A very typical problem of electromechanical position control is an electric motor driving a load that has one dominant vibration mode.
The problem arises in computer-disk-head control, reel-to-reel tape drives, and many other applications. A schematic diagram is sketched in Fig. The motor has an electrical constant Ke , a torque constant Kt , an armature inductance La , and a resistance Ra. The rotor has an inertia J1 and a viscous friction B. The load has an inertia J2. The two inertias are connected by a shaft with a spring constant k and an equivalent viscous damping b.
Write the equations of motion. For the robot in Fig. Determine the dynamic equations relating the speed of the robot with respect to the torque command of the servo. Your equations will require certain quantities, e.
Assume you have access to whatever you. That is, a system where the torque is applied by a motor on a gear that is simply accelerating an attached gear, like the picture in Fig. In order to multiply the torque by a factor of 2, the motor must have a gear that is half the size of the gear attached to the wheel, i.
If the wheel was not attached to the robot, Eq.
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