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| Table of contents |
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| Force Voltage Analogy |
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| Torque Voltage Analogy |
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| Force Current Analogy |
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| Torque Current Analogy |
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Electrical systems and mechanical systems are two physically different systems. There are two types of electrical analogies of translational mechanical systems. Those are force voltage analogy and force current analogy.
Force Voltage Analogy
In force voltage analogy, the mathematical equations of translational mechanical system are compared with mesh equations of the electrical system.
Consider the following translational mechanical system as shown in the following figure.
The force balanced equation for this system is
Consider the following electrical system as shown in the following figure. This circuit consists of a resistor, an inductor and a capacitor. All these electrical elements are connected in a series. The input voltage applied to this circuit is V volts and the current flowing through the circuit is i Amps.
Mesh equation for this circuit is
By comparing Equation 1 and Equation 3, we will get the analogous quantities of the translational mechanical system and electrical system. The following table shows these analogous quantities.
Similarly, there is torque voltage analogy for rotational mechanical systems. Let us now discuss about this analogy.
Torque Voltage Analogy
In this analogy, the mathematical equations of rotational mechanical system are compared with mesh equations of the electrical system.
Rotational mechanical system is shown in the following figure.
The torque balanced equation is
By comparing Equation 4 and Equation 3, we will get the analogous quantities of rotational mechanical system and electrical system. The following table shows these analogous quantities.
Force Current Analogy
In force current analogy, the mathematical equations of the translational mechanical system are compared with the nodal equations of the electrical system.
Consider the following electrical system as shown in the following figure. This circuit consists of current source, resistor, inductor and capacitor. All these electrical elements are connected in parallel.
The nodal equation is
By comparing Equation 1 and Equation 6, we will get the analogous quantities of the translational mechanical system and electrical system. The following table shows these analogous quantities.
Similarly, there is a torque current analogy for rotational mechanical systems. Let us now discuss this analogy.
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Torque Current Analogy
In this analogy, the mathematical equations of the rotational mechanical system are compared with the nodal mesh equations of the electrical system.
By comparing Equation 4 and Equation 6, we will get the analogous quantities of rotational mechanical system and electrical system. The following table shows these analogous quantities.
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FAQs on Electrical Analogies of control systems - Control Systems - Electrical Engineering (EE)
| 1. What is the importance of using analogies in control systems? |  |
| 2. How does the force-voltage analogy work in control systems? | |
Ans. In the force-voltage analogy, force in mechanical systems is analogous to voltage in electrical systems. This analogy helps in translating mechanical concepts into electrical terms for analysis and design.
| 3. What are some common components in electrical analogies of control systems? | |
Ans. Common components in electrical analogies of control systems include resistors representing friction, capacitors representing inertia, and inductors representing compliance.
| 4. How can electrical analogies be used to model and analyze control systems? | |
Ans. By using electrical analogies, control systems can be modeled and analyzed using well-established tools and techniques from electrical engineering, making it easier to understand the behavior of complex systems.
| 5. What are some limitations of using electrical analogies in control systems? | |
Ans. One limitation of using electrical analogies is that not all mechanical components have direct electrical equivalents, leading to simplifications and approximations in the model. Additionally, the analogy may not capture all the nuances of the mechanical system accurately.
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