Integral sliding mode¶
A sliding-mode control design whose integral manifold begins active and rejects bounded matched disturbances.
Core Idea¶
Integral sliding mode control robustifies a nominal controller against bounded disturbances that enter through the control channel. It constructs an integral sliding variable using current state, initial state, and nominal dynamics so that the virtual sliding surface is active from the start. A separate sliding-mode term then counters the matched perturbation, rather than waiting through the reaching phase of conventional sliding control.
The ideal result depends on disturbance matching, an invertible effective control channel, adequate gain, state information, and a mathematical interpretation of discontinuous switching. It is not ordinary integral-error control and does not automatically reject unmatched disturbance or eliminate physical chattering. Applications such as motor speed control test particular designs under particular plant and actuator conditions.
Scope of Application¶
The no-reaching claim belongs to an ideal matched-disturbance design with explicit plant assumptions.
- Robust motor control. Augment nominal speed control against modeled disturbances.
- Nonlinear control design. Separate desired nominal dynamics from uncertainty compensation.
- Observer and output-feedback research. Adapt integral sliding ideas only with separate observability hypotheses.
- Control-theory instruction. Compare reaching-phase and initial-on-surface robustness proofs.
Clarity¶
ISM starts on an integral sliding manifold at t=0, then a robust switching term counters bounded disturbances entering through the input channel. This is not ordinary integration of tracking error. Unmatched disturbances and finite actuator switching need separate treatment.
Manages Complexity¶
An uncertain nonlinear plant combines a desired trajectory with unknown disturbances. The design splits those concerns: nominal controller for planned behavior, sliding compensator for matched uncertainty, and integral surface for initial robustness. This decomposition makes proofs tractable but hides no actuator, sensing, or unmatched-disturbance limitations.
Abstract Reasoning¶
Specify nominal plant and matched disturbance, design u0, define the zero-initialized integral surface, prove ideal sliding with a valid gain, then evaluate sensing and actuator limits.
Knowledge Transfer¶
The method transfers literally among dynamic control plants satisfying the same matched-input and sliding conditions, not to any process with an integral term. An optimizer integrating historical error may share vocabulary but lacks a sliding manifold and disturbance-equivalence proof. The robust-decomposition lesson is broader; the named method remains within nonlinear control theory.
Neighborhood in Abstraction Space¶
Integral sliding mode sits in a moderately populated region (60th percentile for distinctiveness): it has near-neighbors but no dense thicket of look-alikes.
Family — Physical & Geometric Dynamical Quantities (29 abstractions)
Nearest neighbors
- Fourth, fifth, and sixth derivatives of position — 0.86
- Robust Optimization — 0.85
- Circular Cumulative Causation — 0.84
- Time Reversibility — 0.84
- Space Trajectory — 0.84
Computed from structural-signature embeddings · 2026-10-08