scholarly journals The Parameter Variation Problem in State Feedback Control Systems

1965 ◽  
Vol 87 (1) ◽  
pp. 120-124 ◽  
Author(s):  
W. R. Perkins ◽  
J. B. Cruz
Keyword(s):  
Feedback Control ◽  
State Feedback ◽  
Parameter Variation ◽  
Open Loop ◽  
State Feedback Control ◽  
Optimal Feedback Control ◽  
Variation Problem ◽  
Quadratic Performance ◽  
New Interpretation ◽  
Low Sensitivity

The plant-parameter variation problem in multivariable linear systems described by state-vector equations is formulated using a new sensitivity measure. This formulation involves a direct comparison of open-loop and state-feedback performance in the presence of parameter variations and provides a basis for guaranteeing the superiority of the feedback design. Results are obtained for both continuous and discrete multi-input, multi-output systems. Furthermore, it is shown for single-input, multi-output plants that a low-sensitivity design is also an optimal feedback-control design with respect to a quadratic performance index. This provides a new interpretation of a similar result previously obtained by Kalman.

scholarly journals Swing-up control of inverted pendulum systems

Robotica ◽  
1996 ◽  
Vol 14 (4) ◽  
pp. 397-405 ◽  
Author(s):  
Alan Bradshaw ◽  
Jindi Shao
Keyword(s):  
Feedback Control ◽  
State Feedback ◽  
Inverted Pendulum ◽  
Open Loop ◽  
State Feedback Control ◽  
Control Law ◽  
Inverted Position ◽  
Pendulum System ◽  
Inverted Pendulum System ◽  
Partial State

SUMMARYIn Part I a technique for the swing-up control of single inverted pendulum system is presented. The requirement is to swing-up a carriage mounted pendulum system from its natural pendent position to its inverted position. It works for all carriage balancing single inverted pendulum systems as the swing-up control algorithm does not require knowledge of the system parameters. Comparison with previous swing-up controls shows that the proposed swing-up control is simpler, eaiser. more efficient, and more robust.In Part II the technique is extended to the case of the swing-up control of double inverted pendulum systems. Use is made of a novel selective partial-state feedback control law. The nonlinear, open-loop unstable, nonminimum-phase. and interactive MIMO pendulum system is actively linearised and decoupled about a neutrally stable equilibrium by the partial-state feedback control. This technique for swing-up control is not at all sensitive to uncertainties such as modelling error and sensor noise, and is both reliable and robust.

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