# LQ/MPC/Model Predictive Control examples

• leble
In summary, LQ/MPC/Model Predictive Control is a control strategy that uses mathematical models and optimization techniques to predict and adjust the future behavior of a system for optimal performance. It can handle constraints and non-linear systems, adapt to changing conditions, and account for uncertainty. Examples of its application include controlling HVAC systems in buildings and in various industries such as chemical plants, automotive and aerospace control systems, and even in sports equipment.
leble

## Homework Statement

Do you have any idea where i can find (basic) examples of how to derive the cost function
when controlling a system with MPC? Thats it, i feel lost

MPC

## The Attempt at a Solution

Being unfamiliar with MPC (linear quadratic or otherwise), I just checked wiki and it said that you use Euler-Lagrange equations to find the cost-minimizing function. Hope this helps.

## 1. What is LQ/MPC/Model Predictive Control?

LQ/MPC/Model Predictive Control is a control strategy used in engineering and science to optimize the performance of a control system. It involves using mathematical models and optimization techniques to predict the future behavior of a system and adjust the control inputs accordingly to achieve desired performance.

## 2. How does LQ/MPC/Model Predictive Control work?

LQ/MPC/Model Predictive Control works by using a mathematical model of the system, along with measurements of the current state, to predict the future behavior of the system. Based on this prediction, the control inputs are adjusted to achieve the desired performance. This process is repeated in a feedback loop to continuously optimize the system's performance.

## 3. What are the advantages of using LQ/MPC/Model Predictive Control?

Some advantages of LQ/MPC/Model Predictive Control include its ability to handle constraints and non-linear systems, its adaptability to changing conditions, and its ability to account for uncertainty in the system. It can also provide better performance compared to traditional control strategies, especially for complex systems.

## 4. Can you provide an example of LQ/MPC/Model Predictive Control in action?

An example of LQ/MPC/Model Predictive Control in action is the control of a heating, ventilation, and air conditioning (HVAC) system in a building. The control system uses a mathematical model of the building's thermal dynamics, along with temperature and occupancy measurements, to predict future conditions and adjust the HVAC system's inputs to maintain a comfortable and energy-efficient environment.

## 5. What are some real-world applications of LQ/MPC/Model Predictive Control?

LQ/MPC/Model Predictive Control is used in various industries and applications, including process control in chemical plants, automotive and aerospace control systems, robotics, and industrial automation. It is also used in energy management systems, traffic control systems, and even in the control of sports equipment, such as Formula 1 racing cars.

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