π What is Nonlinear Control?
Nonlinear Control is a control strategy designed for systems whose dynamics cannot be accurately described by linear equations. These systems have behaviors like saturation, dead zones, friction, or complex dependencies between inputs and outputs that violate the principle of superposition.
π General Form of Nonlinear System
π₯Μ(t) = f(x(t), u(t))
y(t) = h(x(t), u(t))
x(t): state vectoru(t): control inputy(t): system outputf(Β·)andh(Β·)are nonlinear functions
π€ Why Use Nonlinear Control in Robotics?
- Robots often operate far from equilibrium (e.g., jumping, flying, underwater)
- Dynamic equations involve trigonometric, multiplicative, or non-polynomial terms
- Actuator limits, friction, and contact forces are inherently nonlinear
- Linearization is not always sufficient
π Common Nonlinear Control Techniques
- Feedback Linearization: Cancels nonlinear terms to achieve linear behavior
- Sliding Mode Control: Robust control with discontinuous control action
- Backstepping Control: Recursive design for systems in strict-feedback form
- Lyapunov-Based Control: Ensures stability by designing a Lyapunov function
- Adaptive Control: Handles systems with unknown or changing parameters
β Advantages
- Accurately handles complex and real-world dynamics
- Improved performance and robustness in extreme conditions
- Allows for more aggressive and optimal maneuvers
π« Challenges
- Mathematically more complex
- Requires accurate models of system dynamics
- Stability proofs and controller tuning can be difficult
π Example: Underactuated Robot Arm
A 2-link robotic arm with only one actuator is a nonlinear system. Linear control wonβt work effectively, but nonlinear strategies like energy-based control or backstepping can stabilize the arm even under constraints.
π Summary
- Nonlinear control handles systems with complex behaviors
- Essential for most real-world robotic systems (drones, mobile robots, manipulators)
- Provides robustness, accuracy, and flexibility beyond linear control