Nonlinear control systems - A brief overview of historical and recent advances

Abstract

Last five decades witnessed remarkable developments in linear control systems and thus problems in this subject has been largely resolved. The scope of the present paper is beyond linear solutions. Modern technology demands sophisticated control laws to meet stringent design specifications thus highlighting the increasingly conspicuous position of nonlinear control systems, which is the topic of this paper. Historical role of analytical concepts in analysis and design of nonlinear control systems is briefly outlined. Recent advancements in these systems from applications perspective are examined with critical comments on associated challenges. It is anticipated that wider dissemination of this comprehensive review will stimulate more collaborations among the research community and contribute to further developments.

Computer methods for non-invasive measurement and control of two-phase flows: a review study

“…Besides the theoretical achievements, some works have been performed to design the feedback control solutions based on PID [44,117,4] or PI [107] controllers to demonstrate that this strategy can guarantee the stability of the flows whereas the manual choking occurred insufficiently. The production (subsea) choke is used to control the offshore flow and stabilize the flow line pressure.…”

“…Therefore, in order to satisfy the need for system stability and to optimize production simultaneously some other solutions for flow control were developed. The comprehensive review study of non-linear controller theory together with some examples may be found in [59]. Authors deal with the differential algebra and multivariable calculus to explain the mathematical basis of nonlinear controllers.…”

A Comparative Study of LQR and Integral Sliding Mode Control Strategies for Position Tracking Control of Robotic Manipulators

“…However, a major problem with MPC is that many parameters and coefficients should be properly selected, such as the prediction and control horizons, and also the penalisation factor to obtain satisfactory performance, as concluded by the authors in [25]. Nevertheless, adaptive control offers promising performance with a strong theoretical framework, as in [5], but it produces an aggressive control signal [26], which is particularly harmful to the actuator. Furthermore, the efficiency of adaptive control depends on the effectiveness of the learning scheme.…”

“…SMC is of interest because it can keep the stability of a nonlinear system while maintaining the desired performance by addressing uncertainties in the system [27,28]. However, SMC is too expensive to be used for continuous operation as the control effort of a nonlinear controller scheme is enormous and aggressive, as mentioned in [26,29]. Moreover, SMC suffers from the robustness issue in the reaching phase.…”

Nonlinear Control of a Flexible Joint Robotic Manipulator with Experimental Validation

“…Some methodologies are reported to control the manipulator without taking into account the dynamics of the actuator. Examples include feedback linearization method [7], the singular perturbation approach [8], the integral manifold control [9], the passivity approach [10], the proportional derivative (PD) control approach [7] and the adaptive sliding mode technique [11]. The major limitation of the above-mentioned research works is that these schemes assumed torque to be an input to the rigid link.…”