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How do you learn and update the model of a mechanical system for MPC and feedback control?

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If you want to design a controller for a mechanical system, such as a robot arm, a vehicle, or a wind turbine, you need to have a mathematical model of its dynamics. A model is a set of equations that describe how the system behaves in response to inputs and disturbances. However, models are often uncertain, incomplete, or nonlinear, which makes them difficult to use for control purposes. In this article, you will learn about two approaches to deal with model uncertainty and improve control performance: model predictive control (MPC) and feedback control.

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Edward Mu?oz Garro

Agile Project Manager | Tech & Finance Leader | Scalable Solutions
Dr. Sharanabasava V. Ganachari

School of Advanced Sciences, KLE Technological University, Hubballi-580031

1 What is MPC?

MPC is a control technique that uses a model to predict the future behavior of the system and optimize the control inputs accordingly. MPC works by solving an optimization problem at each time step, where the objective is to minimize a cost function that reflects the desired performance criteria, such as tracking a reference trajectory, avoiding obstacles, or reducing energy consumption. The cost function also includes constraints on the inputs and the states, such as physical limits, safety requirements, or environmental conditions. The optimization problem is solved over a finite horizon, which means that the predictions are made for a limited number of future time steps. The first input from the optimal solution is then applied to the system, and the process is repeated at the next time step with updated measurements and predictions.

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Edward Mu?oz Garro

Agile Project Manager | Tech & Finance Leader | Scalable Solutions
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Incorporating the advantages of MPC, such as its ability to handle constraints and uncertainties, could provide readers with a more comprehensive understanding of its benefits. Additionally, highlighting its adaptability to various system dynamics and its effectiveness in handling nonlinearities could further enrich the comparison with other control techniques.

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Dr. Sharanabasava V. Ganachari

School of Advanced Sciences, KLE Technological University, Hubballi-580031
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To update a mechanical system model for MPC and feedback control: 1. System Identification: Gather operational data, apply methods like least squares to estimate parameters. 2. Model Updating: Adjust parameters to minimize discrepancies between the model and actual performance. 3. Validation: Ensure model accuracy with different datasets. 4. Implementation: Use the updated model in the MPC algorithm. 5. Real-time Updating: Continuously refine the model with new feedback data. This process maintains model accuracy, enhancing control system efficiency and reliability.

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2 What is feedback control?

Feedback control is a control technique that uses a model to estimate the current state of the system and adjust the control inputs accordingly. Feedback control works by measuring or inferring some variables of the system, such as position, velocity, or force, and comparing them with the desired values. The difference between the actual and the desired values is called the error, and it is used to compute the control inputs that will reduce the error. The control inputs are calculated by applying a feedback law, which is a function that relates the error to the inputs. The feedback law can be designed using different methods, such as PID, LQR, or H-infinity.

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Edward Mu?oz Garro

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- PID Control: Adjusts control signal based on current error, past errors, and predicted future trends. - State Feedback Control: Uses feedback from entire system state for comprehensive control. - Adaptive Control: Adjusts controller parameters based on evolving system dynamics.

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3 How to learn and update the model?

MPC and feedback control both require a model of the system, however, this model can be inaccurate or may change over time due to external factors. Therefore, it is important to learn and update the model based on data collected from the system. System identification, machine learning, and adaptive control are all processes that can be used to learn and update the model, depending on the type and complexity of the model and data. System identification uses linear or nonlinear models, and can handle noise and uncertainty in the data. Machine learning utilizes different types of models, such as neural networks or decision trees, and can learn from both supervised and unsupervised data. Adaptive control adjusts the model or feedback law based on the data, and can improve robustness and performance of the controller in uncertain conditions.

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Edward Mu?oz Garro

Agile Project Manager | Tech & Finance Leader | Scalable Solutions
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System identification utilizes parametric and non-parametric methods to fit models to data. Machine learning employs supervised and unsupervised techniques like neural networks and clustering. Reinforcement learning enables systems to learn optimal control strategies. Adaptive control adjusts parameters based on system dynamics using approaches like Model Reference Adaptive Control and model-free methods. Online parameter estimation continuously updates model parameters in real-time. These methods collectively facilitate learning and updating models in MPC and feedback control systems, ensuring adaptability and improved performance.

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4 What are the benefits and challenges of MPC and feedback control?

MPC and feedback control have different benefits and challenges when applied to mechanical systems. MPC can handle constraints and nonlinearities better than feedback control, as it optimizes the inputs over a horizon and accounts for future effects. However, it requires more computational resources and more accurate models than feedback control. On the other hand, feedback control can react faster and more reliably than MPC, but is affected by measurement noise and model errors. Learning and updating the model can improve the performance of both controllers, but can also introduce complexity and instability due to overfitting, bias, or divergence.

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Edward Mu?oz Garro

Agile Project Manager | Tech & Finance Leader | Scalable Solutions
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Recent advancements in MPC and feedback control include: - Machine Learning for Model Improvement: Integration of deep learning and reinforcement learning to enhance system models' accuracy and adaptability. - Efficient Optimization Algorithms for MPC: Development of stochastic, distributed, and online optimization techniques to reduce computational burden while maintaining control performance. These advancements aim to address challenges by improving control accuracy, robustness, and computational efficiency in mechanical systems.

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5 How to choose between MPC and feedback control?

There is no one-size-fits-all answer to which control technique is better for a mechanical system, as this depends on factors such as the system characteristics, the control objectives, the available data, and the computational resources. Nevertheless, some general guidelines can be given: Model Predictive Control (MPC) is more suitable for systems that have complex dynamics, hard constraints, or multiple objectives as it can optimize inputs over a horizon and account for the future effects of the inputs. On the other hand, feedback control is more suitable for systems that have simple dynamics, soft constraints, or single objectives since it can provide fast and reliable responses based on the current state and error of the system. Lastly, learning and updating the model is more suitable for systems that have uncertain, incomplete, or changing models as it can reduce model uncertainty and adapt to changes in the system.

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Edward Mu?oz Garro

Agile Project Manager | Tech & Finance Leader | Scalable Solutions
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Choosing between Model Predictive Control (MPC) and feedback control for a mechanical system depends on factors such as system complexity, constraints, responsiveness requirements, computational resources, model stability, adaptability to uncertainties, feasibility of implementation, and trade-offs between optimization and real-time responsiveness. MPC is favored for systems with complex dynamics, hard constraints, and multiple objectives, while feedback control is preferred for simpler dynamics, faster responses, and limited computational resources. The decision should be guided by a thorough assessment of these factors to ensure the chosen control technique aligns with the system's specific requirements and constraints.

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6 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?

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How do you learn and update the model of a mechanical system for MPC and feedback control?

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1 What is MPC?

2 What is feedback control?

3 How to learn and update the model?

4 What are the benefits and challenges of MPC and feedback control?

5 How to choose between MPC and feedback control?

6 Here’s what else to consider

Mechanical Analysis

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