Quenching And Suppression of Limit Cycles for Achieving Error Free Performance with High Precision in Robotics

The objective of the robotics field is to create intelligent machines that can assist humans in a variety of ways and is keenly associated with automation in utmost precision. The existence/ exhibition of self-sustained nonlinear oscillations termed as limit cycles (LC) limits the performance of most of the physical systems such as the speed and position control in robotics and automation industry as well [1-5]. The importance of prediction of Limit cycles in Multivariable Nonlinear system such as in Robot industry has been widely felt for several decades [1-5]. Quenching of limit cycling oscillations using the method of signal stabilization has gained attention in the beginning of 1960s [6-9] and further discussed in [10-16]. The signal stabilization with high frequency dither signals either deterministic or random for multivariable systems having memory type nonlinearities is a years old problem. Backlash is one of the common memory type nonlinearities that causes exhibition of LC in the system and therefore has been the subject of study since 1940 [2].

Researchers concerned have high precision and efficiency to create intelligent machines of robots. [3,5] they felt the necessity of avoiding LC to have error free performance with high precision. Until [17] no literature was available where systematic discussion for signal stabilization including the process of synchronization, desynchronization in 2x2 memory type nonlinear systems have been addressed. Further a rare literature available which addresses 3x3 nonlinear Multivariable systems, [17-22]. However, a number of industrial problems with two or more higher dimensional configurations, [10] and prediction of LC via describing function methods prove to be quite essential, [10,11,17,23-28]. The prediction of LC in three dimensional nonlinear multivariable systems which can fit the structure of general 3x3 [17,18], nonlinear systems has gained attention in the present scenario.

In the event of existence of limit cycling oscillations the possibility of quenching the sustained oscillations using the signal stabilization technique has been investigated, [12,13] in 2x2 nonlinearity systems with non-memory type nonlinear elements and with memory type Nonlinear elements specifically Backlash type [29] using deterministic signals and also the same has been addressed with Gaussian signal [30] Prediction and suppression of limit cycling oscillations in 2x2 memory type nonlinear systems using arbitrary pole placement has been discussed in [4,31-33] and pole placement using Riccati equation [34,35]Recently, prediction of LC by graphical method in 3x3 Nonlinear systems has been elaborated in [18] and Quenching of LC through signal stabilization using deterministic as well as Gaussian signals. Wherein suppression of LC by pole placement technique either arbitrarily selection of state feedback gain satisfying complete state controllability condition or optimal selection of feedback gain using Riccati Equation and the propositions have been illustrated by digital simulation using a developed programme with MATLAB Codes as well as by use of SIMULINK ToolBox of MATLAB Software.

In the present scenario to achieve best performance in Robotics, Automation Industries, in the event of existence / exhibition of self-sustained oscillations (LC) caused due to the presence of Nonlinearities are to be avoided by quenching/complete extinction through signal stabilization and by suppression through pole placement either arbitrarily selection of state feedback gains or optimal selection using Riccati equation. The Researchers started working in the 1950s to the beginning of 1960s in this area focusing on single input and single output (SISO) systems. Later for the last six to seven decades a lot of literature available where 2x2 multivariable systems with non-memory/memory type nonlinearities have been addressed. In recent years some literature has been available which addresses 3x3 multivariable systems.

The novelty of present discussion claims in: (i) quenching of LC exhibited in nonlinear systems by signal stabilization with deterministic as well as random (Gaussian) signals. Wherein tracking of synchronization, desynchronization has been focused, (ii) suppression of limit cycles in 2x2 and 3x3 multivariable nonlinear systems by pole placement using state feedback with arbitrary selection as well as optimal selection of feedback gain matrix K [17,18,29]. There is an ample scope of extending the present work for signal stabilization as well as for suppression of LC in 3x3 memory type nonlinear systems which may also be subsequently extended for n x n multivariable nonlinear systems to achieve better performance in robotics and automations with utmost precision.

None.

No conflict of interest.

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