June 8, 2023

# What is model predictive control?

Model Predictive Control (MPC) is a sophisticated method for controlling complex systems. It is a mathematical optimization algorithm that predicts the future behavior of a system and generates control actions to achieve a desired performance. MPC is used extensively in process control, automotive and aerospace systems, robotics and automation, energy management, and optimization. In this article, we will provide an overview of the basics of MPC â€“ its definition, key components, algorithm, advantages and limitations.

## Understanding the basics of model predictive control

Model Predictive Control (MPC) is a powerful feedback control strategy that has become increasingly popular in recent years due to its ability to handle complex control problems. MPC is a model-based control approach that uses a predictive model to determine future control actions that optimize a performance index over a specified time horizon. The objective of MPC is to achieve the best possible control performance while satisfying all constraints imposed on the system.

### Definition and purpose of model predictive control

At its core, MPC is a feedback control strategy that optimizes the future performance of a system by predicting the system behavior based on a mathematical model. This predictive model captures the relationships between system inputs and outputs and provides a representation of the system dynamics. By using this model to predict the future behavior of the system, MPC can generate control actions that optimize a performance index over a specified time horizon.

The key advantage of MPC is that it can handle complex control problems that traditional control methods, such as Proportional-Integral-Derivative (PID) control, struggle with. This is because traditional control methods are based on a fixed set of control parameters that are tuned based on empirical knowledge of the process. In contrast, MPC uses a dynamic model of the system to predict its future behavior. This allows MPC to handle multiple inputs and outputs, time-varying constraints, and disturbances. Additionally, MPC can handle nonlinear control problems and provide performance guarantees.

### Key components of model predictive control systems

A model predictive control system consists of several key components that work together to optimize the performance of the system. The first component is the mathematical model of the process. This model captures the relationships between system inputs and outputs and provides a representation of the system dynamics. The second component is the optimizer, which solves an optimization problem that minimizes a performance index while satisfying the constraints imposed on the system. The third component is the cost function, which measures the quality of the control performance. Finally, the controller generates control actions based on the predicted future behavior of the system.

Together, these components work together to optimize the performance of the system. By predicting the future behavior of the system and generating control actions that optimize a performance index over a specified time horizon, MPC can achieve the best possible control performance while satisfying all constraints imposed on the system.

### How model predictive control differs from traditional control methods

As mentioned earlier, traditional control methods, such as PID control, are based on a fixed set of control parameters that are tuned based on empirical knowledge of the process. In contrast, MPC is a model-based control approach that uses a dynamic model of the system to predict its future behavior. This allows MPC to handle complex control problems that traditional control methods struggle with.

Another key difference between MPC and traditional control methods is that MPC can handle nonlinear control problems. Nonlinear control problems are those in which the relationship between the system inputs and outputs is nonlinear. Traditional control methods struggle with these types of problems because they are based on linear models that cannot capture the nonlinear behavior of the system. In contrast, MPC uses a dynamic model of the system that can capture the nonlinear behavior of the system, allowing it to handle nonlinear control problems.

In conclusion, Model Predictive Control (MPC) is a powerful feedback control strategy that uses a predictive model to determine future control actions that optimize a performance index over a specified time horizon. MPC can handle complex control problems that traditional control methods struggle with, and can handle nonlinear control problems. By predicting the future behavior of the system and generating control actions that optimize a performance index over a specified time horizon, MPC can achieve the best possible control performance while satisfying all constraints imposed on the system.

## Applications of model predictive control

Model predictive control (MPC) is a widely used control strategy in various fields, including industrial process control, automotive and aerospace systems, robotics and automation, and energy management and optimization. MPC is a control strategy that uses a mathematical model of the system to predict its future behavior and optimize its performance by adjusting the control inputs.

### Industrial process control

In industrial process control, MPC is used to control various process variables such as temperature, pressure, flow rate, and composition of the process streams. The MPC algorithm takes into account the process model, constraints, and objectives to determine the optimal control inputs that achieve optimal performance, safety, and economic benefits. MPC is widely used in chemical plants, pulp and paper mills, and power plants, where precise control of the process variables is crucial for the efficient operation of the plant.

MPC has several advantages over traditional control strategies such as proportional-integral-derivative (PID) control. MPC can handle nonlinearities, constraints, and uncertainties in the process model, which makes it suitable for complex processes. MPC can also handle multivariable systems, where multiple inputs and outputs are interconnected, and the control variables affect each other. MPC can optimize the control inputs over a horizon, which takes into account the future behavior of the system, and can prevent overshoots and oscillations in the process variables.

### Automotive and aerospace systems

MPC is used in automotive and aerospace systems to control various subsystems such as the engine, transmission, suspension, and aircraft systems. MPC is used to optimize fuel consumption, reduce emissions, improve driver comfort, and enhance safety. MPC can handle the nonlinearities and uncertainties in the system model, which makes it suitable for adaptive control and fault-tolerant control. MPC can also handle the constraints in the system, such as the limits on the control inputs and the physical limitations of the system.

In automotive systems, MPC is used to optimize the powertrain control, such as the engine torque, the transmission gear ratio, and the regenerative braking. MPC can also optimize the vehicle dynamics, such as the yaw rate, the lateral acceleration, and the tire slip. MPC can improve the fuel efficiency, reduce the emissions, and enhance the driving experience. MPC can also handle the uncertainties in the road conditions, such as the changes in the friction coefficient and the slope of the road.

In aerospace systems, MPC is used to optimize the aircraft control, such as the altitude, the airspeed, and the attitude. MPC can also handle the disturbances in the aircraft, such as the turbulence, the wind gusts, and the engine failures. MPC can improve the safety, reduce the fuel consumption, and enhance the passenger comfort. MPC can also handle the constraints in the aircraft, such as the limits on the control surfaces, the fuel consumption, and the weight distribution.

### Robotics and automation

MPC is used in robotics and automation to control the motion, position, and force of robots. MPC is used to optimize trajectory planning, speed control, and force control. MPC can handle the uncertainties and disturbances in the robot environment, such as the changes in the friction, the contact forces, and the external forces. MPC can also handle the constraints in the robot, such as the limits on the joint angles, the velocities, and the torques.

MPC can improve the performance of the robot by optimizing the control inputs over a horizon, which takes into account the future behavior of the robot and the environment. MPC can also handle the nonlinearities in the robot model, such as the friction, the backlash, and the elasticity. MPC can improve the accuracy, the speed, and the robustness of the robot control.

### Energy management and optimization

MPC is used in energy management and optimization to control the operation of power systems, renewable energy systems, and energy storage systems. MPC is used to schedule generation, limit transmission congestion, and balance supply and demand. MPC can also manage energy storage systems and electric vehicles, which can store and discharge energy to balance the grid.

MPC can optimize the energy management by taking into account the uncertainties in the renewable energy sources, such as the solar and wind power. MPC can also handle the constraints in the energy system, such as the limits on the power generation, the transmission capacity, and the energy storage. MPC can improve the efficiency, the reliability, and the sustainability of the energy system.

In conclusion, MPC is a powerful control strategy that can be applied to various fields, such as industrial process control, automotive and aerospace systems, robotics and automation, and energy management and optimization. MPC can handle the nonlinearities, uncertainties, and constraints in the system model, which makes it suitable for complex systems. MPC can optimize the control inputs over a horizon, which takes into account the future behavior of the system, and can improve the performance, safety, and economic benefits of the system.

## The model predictive control algorithm

### Mathematical foundations of model predictive control

The mathematical foundations of MPC are based on dynamic programming and convex optimization. The MPC algorithm involves the solution of a quadratic programming (QP) problem at each time step to determine the optimal control actions. The QP problem is subject to constraints imposed on the system, such as input/output limits, rate-of-change constraints, and state-space constraints.

### Steps in the model predictive control algorithm

The MPC algorithm involves several steps, including system identification, model formulation, cost function design, constraint specification, state estimation, trajectory generation, and control law computation. These steps are iterative, and the MPC algorithm is updated with new process measurements at each time step.

### Tuning parameters for optimal performance

Optimal tuning of the MPC parameters is critical for achieving good control performance. The tuning process involves adjusting the weights of the cost function, selecting the prediction horizon and control horizon, and specifying the constraints. There are several methods for tuning the MPC parameters, including trial-and-error, offline optimization, and online adaptation.

## Advantages and limitations of model predictive control

### Benefits of using model predictive control

MPC provides several benefits over traditional control methods. MPC is a model-based control approach that can handle complex control problems, such as those involving multiple inputs and outputs, time-varying constraints, and disturbances. MPC can also provide good control performance while satisfying constraints, and it can handle nonlinear control problems and provide performance guarantees.

### Challenges and drawbacks of model predictive control

MPC has several challenges and limitations. MPC requires a dynamic model of the process, which can be difficult to obtain or may require significant effort to derive. The MPC algorithm involves solving an optimization problem at each time step, which can be computationally expensive. MPC can also be sensitive to model uncertainties, disturbances, and measurement noise, and the performance of the controller can degrade if the model is inaccurate.

### Overcoming limitations through advanced techniques

Recent advances in MPC have addressed some of the limitations and challenges of this control method. Techniques such as Model Predictive Static Programming (MPSP), robust MPC, distributed MPC, and adaptive MPC have been developed to improve the performance and applicability of MPC. These techniques can handle more complex control problems, reduce computational burden, and handle uncertainties and disturbances more effectively.

## Conclusion

In conclusion, Model Predictive Control is a powerful method for controlling complex systems. MPC is a model-based control approach that uses a mathematical model of the process to predict the future behavior of the system and generate control actions that optimize performance over a specified time horizon. MPC has several advantages over traditional control methods, including the ability to handle nonlinear control problems, provide performance guarantees, and satisfy complex constraints. However, MPC also has some challenges and limitations, such as the need for accurate models, high computational cost, and sensitivity to disturbances and measurement noise. Advanced techniques are being developed to overcome these limitations and make MPC more robust and adaptable in a wide range of control applications.