Minimization of the Peak-to-Peak Gain in Periodic Systems Under Full State Feedback1

1985 ◽  
Vol 123 (1) ◽  
pp. 10-20 ◽  
Author(s):  
Johannes Aubrecht ◽  
Petros G. Voulgaris
Keyword(s):  
Linear Time ◽  
Periodic Case ◽  
Linear Programs ◽  
Nonlinear Controller ◽  
State Space Approach ◽  
Linear Time Invariant ◽  
Full State ◽  
Linear Time Invariant Systems ◽  
Time Invariant ◽  
Finite Linear

The paper considers the minimization of the l∞-induced norm of the closed loop in linear periodically time varying (LPTV) systems when state information is available for feedback. A state-space approach is taken and concepts of viability theory and controlled invariance are utilized. It is shown that a memoryless periodically varying nonlinear controller can be constructed to achieve near-optimal performance. The construction involves the solution of several finite linear programs and generalizes to the periodic case earlier work on linear time-invariant systems (LTI).

Chattering-Free Error Integral Driven MIMO Sliding Mode Regulator for Linear Time-Invariant Systems

2016 ◽  
Vol 138 (7) ◽  
Author(s):  
Kerim Yunt
Keyword(s):  
Boundary Layer ◽  
Sliding Mode ◽  
Linear Time ◽  
Optimization Procedure ◽  
Pole Placement ◽  
Linear Time Invariant ◽  
Full State ◽  
Chattering Free ◽  
Linear Time Invariant Systems ◽  
Time Invariant

In this work, an error-integral-driven sliding mode controller (EID-SMC) is discussed for multi-input multi-output (MIMO) linear time-invariant (LTI) systems. The boundary layer approach is utilized in order to eliminate the chattering problem. Though the sliding variable remains in the vicinity of the sliding surface without reaching it, it is shown that the steady-state error vanishes exponentially asymptotically within a boundary layer, for systems of relative order one, even if parameter uncertainty and unmatched input disturbances exist. The pole placement is accomplished indirectly with an iterative optimization procedure by considering limits on controls and state. Finally, the output-feedback controller is augmented with a Luenberger full-state and disturbance observer.

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