How can you simplify feedback control without sacrificing performance?

1 Use PID controllers

One of the most common and effective ways to simplify feedback control is to use proportional-integral-derivative (PID) controllers. PID controllers are simple algorithms that calculate the error between the desired and actual values of a variable, and then apply a correction based on three parameters: proportional, integral, and derivative. PID controllers can be tuned to achieve a balance between speed, accuracy, and stability of the system. They can also be implemented easily on microcontrollers or other hardware platforms.

2 Apply linearization methods

Another technique to simplify feedback control is to apply linearization methods to nonlinear systems. Nonlinear systems are systems that do not obey the principle of superposition, meaning that the response of the system to a combination of inputs is not equal to the sum of the responses to each input separately. Nonlinear systems can be challenging to analyze and control, as they may exhibit complex behaviors such as chaos, bifurcations, or hysteresis. Linearization methods are mathematical tools that approximate a nonlinear system by a linear system around a certain operating point or region. Linear systems are easier to control, as they can be represented by matrices and vectors, and can be manipulated using standard techniques such as eigenvalues, eigenvectors, and state-space models.

3 Use model reduction techniques

A third way to simplify feedback control is to use model reduction techniques to reduce the complexity and dimensionality of the system. Model reduction techniques are methods that aim to find a simpler representation of the system that preserves its essential features and dynamics. Model reduction techniques can be useful for systems that have many inputs, outputs, states, or parameters, or that are coupled with other systems. Model reduction techniques can be classified into two categories: projection-based methods and approximation-based methods. Projection-based methods project the original system onto a lower-dimensional subspace, while approximation-based methods approximate the original system by a simpler one using various criteria such as error minimization, frequency response matching, or stability preservation.

4 Use adaptive or learning-based control

A fourth option to simplify feedback control is to use adaptive or learning-based control. Adaptive or learning-based control are methods that allow the controller to adjust its parameters or behavior based on the feedback from the system or the environment. Adaptive or learning-based control can be useful for systems that are uncertain, time-varying, nonlinear, or subject to disturbances or noise. Adaptive or learning-based control can be based on various approaches, such as artificial neural networks, fuzzy logic, genetic algorithms, reinforcement learning, or Bayesian inference.

5 Use feedback linearization

A fifth and final technique to simplify feedback control is to use feedback linearization. Feedback linearization is a method that transforms a nonlinear system into a linear system by applying a nonlinear feedback law. Feedback linearization can be seen as a generalization of linearization methods, as it does not require a specific operating point or region, but rather applies to the whole system. Feedback linearization can be achieved by using various methods, such as input-output linearization, input-state linearization, or exact linearization. Feedback linearization can provide better performance and robustness than linearization methods, as it can cancel out the nonlinearities of the system completely.

Feedback control is a vital skill for robotics, but it does not have to be complicated or difficult. By using these techniques and tips, you can simplify feedback control without sacrificing performance, and make your robots more efficient, reliable, and intelligent.

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?