What Is the Sliding Mode Controller Reaching Law & Chattering Calculator?
Sliding mode control drives system states to a switching surface s = 0 and keeps them there using high-frequency discontinuous feedback.
How Does the Sliding Mode Controller Reaching Law & Chattering Calculator Work?
The reaching phase drives s(0) to zero in finite time t_reach = |s(0)| / K; on the surface, system dynamics are completely invariant to matched disturbances.
Sliding Mode Controller Reaching Law & Chattering Calculator Formula & Variables
The core mathematical equation utilized by this calculator is expressed as:
s = c x_1 + x_2, quad dot{s} = -K operatorname{sgn}(s), quad t_{ ext{reach}} = rac{|s(0)|}{K}
Constant-rate reaching law dynamics and reaching time to sliding manifold.
How to Use the Sliding Mode Controller Reaching Law & Chattering Calculator
- Input initial states (x1, x2), sliding surface coefficient c, switching gain K, and boundary layer thickness phi.
Step-by-Step Example Calculation
Inverted Pendulum Sliding Mode Regulation
Input Values:
initialStateX1:2
initialStateX2:-1
slidingCoeffC:3
switchingGainK:5
boundaryLayerThicknessPhi:0.15
Worked Steps: Initial sliding variable s(0) = 5.0, Reaching time = 1.00 s, Chattering suppressed within boundary layer phi = 0.15.
Understanding Your Result
Displays reaching time in seconds, initial sliding variable s(0), and boundary layer smoothing parameter.
Factors That Affect the Result
- Higher switching gain K speeds reaching but exacerbates physical actuator chattering; boundary layers smooth chattering into quasi-sliding.
When Should You Use This Calculator?
- Electric motor drives, robotics manipulators, aerospace flight control, and power inverters subject to parameter uncertainty.
Assumptions & Limitations
- Assumes matched disturbances satisfy bounds within switching gain K.
Frequently Asked Questions
Calculation Accuracy & Reference Note
Standard Slotine & Li variable structure control formulation.