Question 10.3.7: Controlling the Speed of a Conveyor A conveyor drive system ...

System Dynamics

Controlling the Speed of a Conveyor

A conveyor drive system to produce translation of the load is shown in Figure 10.3.11. To translate the load a specified distance, the drive wheels must rotate through a required angle, and this can be accomplished by controlling the speed, often with a trapezoidal speed profile. The equivalent inertia of the load and all the drive components felt at the motor shaft is $I_{e}$ . The effect of Coulomb friction in the system produces an opposing torque $T_{Fe}$ at the motor shaft, and the damping in the system is negligible. Develop the block diagram of a proportional control system using an armature-controlled motor for this application. Assume that the drive wheel speed $ω_{L}$ is measured by a tachometer and that the motor speed $ω_{m}$ is related to the drive wheel speed by $ω_{m} = N ω_{L}$ , where N is the speed ratio due to the reducer and the chain drive.

10.3.11

The "Step-by-Step Explanation" refers to a detailed and sequential breakdown of the solution or reasoning behind the answer. This comprehensive explanation walks through each step of the answer, offering you clarity and understanding.
Our explanations are based on the best information we have, but they may not always be right or fit every situation.

The blue check mark means that this solution has been answered and checked by an expert. This guarantees that the final answer is accurate.
Learn more on how we answer questions.

This Question has been Answered.

Already have an account?

Related Answered Questions

Question: 10.7.2

Design of a PD Control System For the system shown in Figure 10.7.1, we are given that I = 10 and c = 2. The dominant time constant τ is specified to be 2 s, and the damping ratio is specified to be ζ = 1. a. Compute the required values for KP and K D. Evaluate the steady-state command error and ...

Verified Answer:

a. From the figure we obtain the following output,...

Question: 10.7.1

PD Control of a Neutrally Stable Second-Order Plant PD control of a neutrally stable second-order plant is shown in Figure 10.7.1. Investigate its performance for step and ramp inputs for c ≥ 0. ...

Verified Answer:

The output equation is

\Theta(s) = \frac{K_...

Question: 10.6.4

Use of Internal Feedback Suppose the plant to be controlled is G p(s) = 1/I s + c where I = 5 and c = 2. Figure 10.6.6 shows a proposed alternative to PI control for this plant. It uses an internal feedback loop to adjust the output of the controller. The dominant time constant is specified to be ...

Verified Answer:

a. From the figure, we obtain the output equation ...

Question: 10.6.3

Computing PI Gains A PI control system is shown in Figure 10.6.2. Suppose the plant has the parameter values I = 5 and c = 2. The dominant time constant is specified to be 0.5 s. a. Compute the required values for KP and KI for each of the following three cases: (1) ζ = 0.707, (2) ζ = 1, and (3) ...

Verified Answer:

From the block diagram we obtain the following out...

Question: 10.6.2

Response of a Proportional Control System Suppose the plant shown in Figure 10.6.1 has the parameter values I = 5 and c = 2 in a consistent set of units in which time is measured in seconds. (a) Determine the smallest value of the gain KP required so that the steady-state command error will be no ...

Verified Answer:

a. The error equation is

E(s) = \Omega_{r}(...

Question: 10.6.1

Proportional Control of a First-Order Plant Consider proportional control of the first-order plant whose transfer function is 1/(Is +c). This can represent a rotational system whose model is Iω˙ + cω = T − Td , where the controlled variable is the speed ω, the actuator torque is T , and the ...

Verified Answer:

The transfer functions are

\frac{\Omega(s)}...

Question: 10.4.2

Hydraulic Implementation of PI Control Figure 10.4.5 shows a hydraulic system whose input is the motion y. Show that this system implements PI action, if the inertia of the load is small. ...

Verified Answer:

For small motions,

z = \frac{L_{2}}{L_{1} ...

Question: 10.4.1

Hydraulic Implementation of Proportional Control Figure 10.4.3 shows a hydraulic implementation of proportional action to control the angle of an aircraft rudder, elevator, or aileron (see [Cannon, 1967]). The input motion y is produced by the motion of the pilot’s control stick acting through ...

Verified Answer:

When the input motion y occurs, the beam pivots ab...

Question: 10.3.8

Controlling the Position of a Robot Arm Link The drive system for one link of a robot arm is illustrated in Figure 10.3.13. The equivalent inertia of the link and all the drive components felt at the motor shaft is Ie. Gravity produces an opposing torque that is proportional to sin θ but which we ...

Verified Answer:

The dynamics of the mechanical subsystem are descr...

Question: 10.3.6

Effect of Negligible Armature Time Constant Derive the transfer functions for the case where the armature time constant La/Ra is small ...

Verified Answer:

If

T_{L} = 0

, we obtain Figure 10.3...