Sliding Mode Controlfor Robust Regulationof Chemical Processes

This paper concerns the problems of robust stability analysis and stabilization for uncertain linear system with time-varying delay. In order to obtain a robust stability criterion with less conservative for uncertain linear delay system, a quadratic integral inequality is improved by matrix decomposition. Further, two different kinds of controller, i.e., linear memoryless state feedback controller and linear state feedback controller with state delay, are derived in terms of the robust stability criteria. Two numeral examples are provided to demonstrate the validity of the proposed methods.

The stabilization problem of linear time-varying uncertain delay systems by means of linear constant memoryless state feedback control is investigated here. In the case when uncertain parameters may vary independently in arbitrarily large bounding sets, the locations of uncertain elements in the system parameters play an important role. So far obtained conditions of this problem have been found to have a particular geometric configuration with respect to the permissible locations of uncertain elements. In this paper, such a previously obtained configuration is developed to a basic form of antisymmetric stepwise configuration which is a necessary and sufficient condition for time-varying uncertain systems without delays to be quadratically stabilizable by means of linear constant state feedback control. It is shown that if a given system satisfies such developed conditions then the system is stabilizable via linear constant state feedback control with regardless to the upper bounds of time-varying uncertain parameters and time-varying delays

In this paper, advanced interval type-2 fuzzy sliding mode control (AIT2FSMC) for robot manipulator is proposed. The proposed AIT2FSMC is a combination of interval type-2 fuzzy system and sliding mode control. For resembling a feedback linearization (FL) control law, interval type-2 fuzzy system is designed. For compensating the approximation error between the FL control law and interval type-2 fuzzy system, sliding mode controller is designed, respectively. The tuning algorithms are derived in the sense of Lyapunov stability theorem. Two-link rigid robot manipulator with nonlinearity is used to test and the simulation results are presented to show the effectiveness of the proposed method that can control unknown system well.

A novel procedure is presented to design a linear constant state feedback controller with a prespecified performance measure. The method is an iterative technique based on the sensitivity of a quadratic cost functional with respect to the feedback gains. At each iteration, a Riccati-type algebraic matrix equation is solved to compute the sensitivity expressions needed to update the feedback gains.

This article describes the design of a linear observer–linear controller-based robust output feedback scheme for output reference trajectory tracking tasks in the case of nonlinear, multivariable, nonholonomic underactuated mobile manipulators. The proposed linear feedback scheme is based on the use of a classical linear feedback controller and suitably extended, high-gain, linear Generalized Proportional Integral (GPI) observers, thus aiding the linear feedback controllers to provide an accurate simultaneous estimation of each flat output associated phase variables and of the exogenous and perturbation inputs. This information is used in the proposed feedback controller in (a) approximate, yet close, cancelations, as lumped unstructured time-varying terms, of the influence of the highly coupled nonlinearities, and (b) the devising of proper linear output feedback control laws based on the approximate estimates of the string of phase variables associated with the flat outputs simultaneously provided by the disturbance observers. Simulations reveal the effectiveness of the proposed approach.

In this paper, a novel adaptive interval type-2 fuzzy sliding mode control (AIT2FSMC) methodology is proposed based on the integration of sliding mode control and adaptive interval type-2 fuzzy control for chaotic system. The AIT2FSMC system is comprised of a fuzzy control design and a hitting control design. In the fuzzy control design, an interval type-2 fuzzy controller is designed to mimic a feedback linearization (FL) control law. In the hitting control design, a hitting controller is designed to compensate the approximation error between the FL control law and the interval type-2 fuzzy controller. The parameters of the interval type-2 fuzzy controller, as well as the uncertainty bound of the approximation error, are tuned adaptively. The adaptive laws are derived in the sense of Lyapunov stability theorem, thus the stability of the system can be guaranteed. The proposed control system compared to adaptive fuzzy sliding mode control (AFSMC). Simulation results show that the proposed control systems can achieve favorable performance and robust with respect to system uncertainties and external disturbances.

The increasing use of nonlinear loads entails serious electrical energy quality problems in power grids. Active power filter could lead to significant improvement in harmonic compensation performance. In this paper, an adaptive second-order sliding mode fuzzy control based on linear feedback strategy for a three-phase active power filter is proposed to eliminate harmonics. This scheme is constituted by adaptive controller, second-order sliding mode controller, fuzzy controller, and linear feedback controller. The linear feedback controller can compensate the system’s nonlinearities and make the new system have a linear behavior between the input and output. Moreover, the second-order sliding mode controller could transfer the discontinuities in the controller and reduce system chattering. Simulation results illustrate the proposed controller has better performance compared with fuzzy control and adaptive sliding mode fuzzy control.

Gain-scheduled Composite Non linear Feedback (CNF) control has been implemented to Continuous Stirred Tank Reactor (CSTR) in this work. Chemical reaction takes place inside the CSTR, which is adjured from high residual concentration to low residual concentration. Control of CSTR is a bit complex, as it requires complete dynamic study and its implementation. During the entire process, the reaction kinetics changes from stable-unstable-stable range with the decrease in residual concentration. To stabilize the reaction, appropriate cooling is necessary, to ensure that overheating of the CSTR doesn't occur. Gain-scheduled composite non linear feedback controller has been implemented successfully for better tracking performance and error has been computed in terms of Integral of Absolute Error (IAE). The novelty of the work lies in lesser error obtained for this particular model of CSTR. Comparison of the IAE has been done with Model Reference Adaptive Control (MRAC) MIT control in CSTR.

In this paper the problem of stabilizing a linear timeinvariant system with quantized feedback is addressed. We focus on systems with rectilinear quantization where only some of the outputs are quantized either by limited sensor precision or data rate constraints and the rest of the output is sent to the controller without quantization. We call these systems partly-quantized feedback systems. Aside from the rectilinear boxes that we know output resides in, we determine moving hyperplanes in output space such that exact value of output has to lie on these planes too. Using the intersection of rectilinear boxes and hyperplanes, we find the best estimate of output to be used in linear feedback controllers and hence we reduce the maximum quantization error and find a smaller invariant region around origin. A simulation of the proposed controller is also presented.

Recently, magnetic telemanipulation devices have shown a great deal of promise in such areas as semi-conductor manufacturing, wind tunnels, drug delivery, and many more. However, these devices are generally associated with problems caused by payload variation and uncertainties in the parameters of the system which in turn, have limited the development and application of magnetic telemanipulation technology to its full capacity. This paper addresses and deals with these issues by implementation of a precise position control method for a magnetic telemanipulation system with high level of uncertainties in its parameters. The levitation system used in this study is primarily designed for performing remote pick and place operations. The levitated object is a 28 gr microrobot capable of grasping and releasing payloads as heavy as 8 gr. To cope with the uncertainties in the modeling and payload variation, a model reference adaptive feedback linearization (MRAFL) controller is designed and its performance compared with an ordinary feedback linearization (FL) controller. Through experimental results it is shown that the MRAFL controller enables the microrobot to grasp and transport a payload as heavy as 30% of its own weight without a considerable effect on its positioning accuracy. In the presence of the payload, the MRAFL controller resulted in a RMS positioning error of 8 μm} compared with 27.9 μm} of the FL controller. The approach presented in this work is versatile as it leads to the modeling and control of a highly nonlinear system through a modular approach that can be applied to a variety of magnetic levitation and telemanipulation systems.

This paper addresses the problem of designing low-order and linear robust feedback controllers that providea prioriguarantees with respect to stability and performance when applied to a fluid flow. This is challenging, since whilst many flows are governed by a set of nonlinear, partial differential–algebraic equations (the Navier–Stokes equations), the majority of established control system design assumes models of much greater simplicity, in that they are: firstly, linear; secondly, described by ordinary differential equations (ODEs); and thirdly, finite-dimensional. With this in mind, we present a set of techniques that enables the disparity between such models and the underlying flow system to be quantified in a fashion that informs the subsequent design of feedback flow controllers, specifically those based on the$\mathscr{H}_{\infty }$loop-shaping approach. Highlights include the application of a model refinement technique as a means of obtaining low-order models with an associated bound that quantifies the closed-loop degradation incurred by using such finite-dimensional approximations of the underlying flow. In addition, we demonstrate how the influence of the nonlinearity of the flow can be attenuated by a linear feedback controller that employs high loop gain over a select frequency range, and offer an explanation for this in terms of Landahl’s theory of sheared turbulence. To illustrate the application of these techniques, an$\mathscr{H}_{\infty }$loop-shaping controller is designed and applied to the problem of reducing perturbation wall shear stress in plane channel flow. Direct numerical simulation (DNS) results demonstrate robust attenuation of the perturbation shear stresses across a wide range of Reynolds numbers with a single linear controller.

In this paper a new linear state feedback controller for artificial pancreas is proposed to regulate the blood glucose level in diabetic patients. Diabetes mellitus is a family of chronic metabolic diseases in which body's blood glucose regulatory system doesn't function properly. In this study, Bergman's minimal model has been used as a base model, to reformulate dynamics of insulin and glucose concentrations in blood's plasma as a constrained polynomial dynamical system. Since it is hard to derive exact value of parameters in most biological systems, all parameters of the model has been considered uncertain and therefore parametric uncertainty has been exploited in control design. Based on sum of squares technique, a linear state feedback controller has been obtained to regulate the blood's insulin and glucose concentration levels around the basal levels. Main achievements of this paper are simplicity of controller structure which makes it easy to implement, parametric uncertainty to cover more patients and patient-nonspecific design, and employment of nonlinear techniques without any simplifications.

In this paper, the control of chaos with a single controller, which provides simplicity in implementation, is investigated in continuous time nonlinear Rucklidge system. For this purpose, a linear feedback controller and a passive controller are constructed and added to the Rucklidge chaotic system. Lyapunov function is used to realize that the controller ensures the global asymptotic stability of the system. Owing to the controller, Rucklidge chaotic system can be regulated to its equilibrium points. Numerical simulations of the proposed methods and local relay control method have been demonstrated, compared and discussed.

There are many types of controllers had been used to control Autonomous Underwater Vehicle (AUV) such as Proportional Integral Derivative (PID), Linear Quadratic Regulator (LQR), state feedback linearization, integrator back-stepping, and Sliding-Mode Control (SMC). However, for PID and SMC in particular, it is difficult to determine the optimal control design parameters. The objective of this study is to design and develop a responsive motion control system with optimal parameters for an AUV. The contribution of this paper is in term of introducing a filter to smooth reference signal and proposing a brute forcing technique to find optimal controller parameters. The methodology starts with modeling the AUV, estimating the unknown parameters from a real AUV model, designing a control system based on PI and SMC methods, and finally optimizing the controller parameters. The controller design was onto controlling surge speed using PI, heading using SMC, and diving using SMC. Simulation-wise, the developed control system has an average value of 93.89 % of responsiveness to track desired trajectory while 82.33 % of responsiveness without using the smoothing filter. The tested input signals were unit step, ramp, parabolic, and sinusoidal.

The designs of two linear control systems approach to stabilize the balance of an unmanned bicycle system are presented. Both approaches are based on the use of a reaction wheel or flywheel to balance the bicycle. The two linear control approaches, based on the linearization of a nonlinear model obtained using Lagrange formalism, are the classic linear controllers, PID and State Feedback control. The performance of both controllers is verified by digital simulation and real-time experimental results.