Name: cruise control and aircraft system models
Uploaded: 2024-11-21T14:54:07.000Z
Duration: 1 min 22 s
Channel: JoVE

Cruise control in cars, a multi-input system, adjusts to the driver&#39;s speed preference and compensates for uphill disturbances.
The block diagram for this system includes the desired speed and the disturbance as inputs.
When the disturbance is nullified, the block diagram simplifies to a specific transfer function. When the primary input signal is nullified, the block diagram yields another transfer function.
The system&#39;s overall response is the sum of the responses due to the disturbance and input signals.
An airplane is a multi-variable system with multiple inputs and outputs, like the flight controls and the plane&#39;s movement.
Block diagrams can illustrate each input and output, while a simplified version employs vectors to represent multiple inputs and outputs.
These systems can also be depicted using feedback, where the relationships between the different parts of the system are expressed in a matrix form.
By solving these equations, the closed-loop transfer matrix gives the final relationship between the output and input.
Consider specific matrices for the transfer functions. Upon substitution, the closed-loop transfer function matrix can be calculated.

multi-input and multi-variable systems

Multi-input and Multi-variable systems

Cruise control systems in cars are designed as multi-input systems to maintain a driver's desired speed while compensating for external disturbances such as changes in terrain. The block diagram for a cruise control system typically includes two main inputs: the desired speed set by the driver and any external disturbances, such as the incline of the road. By adjusting the engine throttle, the system maintains the vehicle's speed as close to the desired value as possible.
In the absence of disturbances, the cruise control system's block diagram can be simplified to a specific transfer function. This transfer function represents the relationship between the desired speed input and the vehicle's actual speed.
<img alt="Transfer function equation \( T_d(s) = \frac{Y(s)}{R(s)} \), diagram for control systems analysis." src="/files/ftp_upload/16107/16107_PT_equation_001.svg" style="height: 36px;" data-altupdatedat="1762173717000" data-alt="Equation1" />
where Td(s) is the transfer function from the desired speed R(s) to the actual speed Y(s).
Conversely, when the primary input signal (the desired speed) is nullified, the block diagram simplifies to another transfer function, representing the system's response to external disturbances alone.
<img alt="Control system transfer function Tu(s)=Y(s)/D(s) formula, mathematical equation." src="/files/ftp_upload/16107/16107_PT_equation_002.svg" style="height: 52px;" data-altupdatedat="1762173717000" data-alt="Equation2" />
where Tu(s) is the transfer function from the disturbance D(s) to the actual speed Y(s).
The overall response of the cruise control system is the superposition of the responses to both the desired speed and the disturbance inputs. This can be mathematically represented as:
<img alt="Control system equation Y(s)=Td(s)R(s)+Tu(s)D(s); transfer function; formula for system output." src="/files/ftp_upload/16107/16107_PT_equation_003.svg" style="height: 30px;" data-altupdatedat="1762173717000" data-alt="Equation3" />
This superposition principle illustrates how the system adjusts to maintain the desired speed while counteracting disturbances.
In a more complex system, such as an airplane, multiple inputs and outputs must be considered. Inputs might include control signals from the pilot, such as aileron, rudder, and elevator adjustments, while outputs are the aircraft's responses, such as changes in roll, pitch, and yaw. The complexity of such a system necessitates the use of vectors and matrices to represent the multiple inputs and outputs succinctly.
Block diagrams for multi-variable systems like airplanes can be simplified using vector representations. Inputs and outputs are expressed as vectors, and their relationships are captured in a transfer matrix. Feedback loops in these systems can also be described using matrix equations, allowing for a comprehensive representation of the system's dynamics.

Cruise control in cars, a multi-input system, adjusts to the driver&#39;s speed preference and compensates for uphill disturbances.
The block diagram for ...

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Electrical Engineering

Unit 1

Diagrams and Signal Flow Graphs

KEY TERMS AND CONCEPTS

cruise control and aircraft system models

Cruise control systems show how a control system can handle more than one input. In a car, the driver sets a desired speed, and the system also responds to outside disturbances such as changes in road slope. The throttle is adjusted so the vehicle speed stays as close as possible to the target value.

When the disturbance is ignored, the cruise control block diagram can be reduced to a transfer function. This transfer function describes how the desired speed input, R(s), affects the actual speed output, Y(s). When the desired speed signal is set to zero, the diagram can be reduced in a different way. That case gives the transfer function for the disturbance input, D(s), to the vehicle speed, Y(s).

The full system response comes from adding these two responses together. This is the principle of superposition. It shows how the cruise control system works to track the driver’s setting while also reducing the effect of disturbances.

More complex systems, such as airplanes, have multiple inputs and outputs. The pilot may change the aileron, rudder, and elevator, and the aircraft responds with roll, pitch, and yaw. Because there are several signals on both sides, vectors and matrices are used to write the system in a compact form.

In these multi-variable systems, inputs and outputs are grouped into vectors. Their relationships are described with a transfer matrix. Feedback loops can also be written with matrix equations. This gives a complete way to represent how the system behaves.

Cruise Control and Aircraft System Models

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Cruise control systems show how a control system can handle more than one input. In a car, the driver sets a desired speed, and the system also responds to outside disturbances such as changes in road slope. The throttle is adjusted so the vehicle speed stays as close as possible to the target value. When the disturbance is ignored, the cruise control block diagram can be reduced to a transfer function. This transfer function describes how the desired speed input, R(s), affects the actual...

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key terms and concepts

Learn how cruise control uses multiple inputs, transfer functions, and superposition, and how airplanes use vectors and matrices to model roll, pitch, and yaw.

Cruise Control and Aircraft System Models | JoVE K12

JoVE Core Electrical Engineering offers easy-to-understand animated videos that cover fundamental concepts of electric circuits along with circuit analysis techniques. It incorporates first-order and second-order circuits using operational amplifiers and circuit transformation concepts. The inclusion of practical design examples and real-world applications through scientist-in-action videos adds significant educational value, making complex concepts accessible.

electrical engineering

Cruise Control and Aircraft System Models

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