MIMO Second Order Sliding Mode Control

Department of Defense Regulation requires designers to evaluate the robustness of their designs using phase and gain margin criteria. Given that such criteria are applicable to linear designs, their inapplicability in their current definition to Higher Order Sliding Mode (HOSM) control designs; non-linear designs techniques in the time domain appeared to constitute a major hindrance to the application of HOSM techniques to aircraft and missiles. This paper illustrates the usage of new phase and gain margin techniques applicable to HOSM designs for providing measures of robustness such designs. The technique consists in replacing the -1 singularity point used with linear designs with describing function based representations of the HOSM controller. It is applied here to general problem of guidance of aerospace vehicles steered with aerodynamic lift that is, to a control problem with relative degree = 3. In the application case we assume the unavailability of attitude measurements. Results show that whether the guidance enforces the collision condition or a proportional integral linear manifold has little effect on the robustness. The concept of practical Relative Degree is introduced and applied instead of the strict definition thereof.

In this paper, an adaptive neural network (NN) tracking controller is developed for a class of uncertain multi-input multi-output (MIMO) nonlinear systems with input saturation. Radial basis function neural networks are utilized to approximate the unknown nonlinear functions in the MIMO system. A novel auxiliary system is developed to compensate the effects induced by input saturation (in both magnitude and rate) during tracking control. Endowed with a switching structure that integrates two existing representative auxiliary system designs, this novel auxiliary system improves control performance by preserving their advantages. It provides a comprehensive design structure in which parameters can be adjusted to meet the required control performance. The auxiliary system signal is utilized in both the control law and the neural network weight-update laws. The performance of the resultant closed-loop system is analyzed, and the bound of the transient error is established. Numerical simulations are presented to demonstrate the effectiveness of the proposed adaptive neural network control.

The main purpose of this paper is to design a robust second order sliding mode controller that can deal with uncertain nonlinear systems. This controller can keep the main advantages of the first order sliding mode controller, such as the ability to make the system asymptotically stable by forcing the error and its derivatives to have a zero value, the simplicity in the operation, and the robustness in the existence of perturbations. In spite of the features that characterize the first order sliding mode controller (1 SMC), it still suffers from the unwanted phenomenon “chattering”, which originates from a discontinuous control part (sign function). In this context, saturation function can be used instead of sign function to reduce this problematic chattering. Different from the saturation function method, the second order sliding mode controller can be used to overcome the chattering; suffered by the first order sliding mode controller and to retain the stability and performance of the system. In this paper, the twisting and the super twisting second-order algorithms of the sliding mode controller were used, and their results were compared with the first order sliding mode controller. So, this subject focused on the chattering problem who suffers from it the 1 SMC and try to reduce it by using the 2 SMC, the uncertain pendulum system was adopted in this work for the purpose of checking the three controllers. The simulations results showed that the second order sliding mode controller has the ability to reduce both the chattering magnitude and the steady state error and achieve an asymptotically stable system. The results were obtained by using MATLAB programming.

An optimal adaptive actuator failure compensation control scheme is proposed for a class of multi-input multi-output (MIMO) uncertain nonlinear continuous-time systems with redundant actuators subject to uncertain failures. Only single neural network is used in the proposed adaptive dynamic programming (ADP) scheme to simultaneously learn the infinite horizon cost function and the approximate optimal control input that minimizes the Hamilton-Jacobi-Bellman (HJB) equation. Besides, an uncertainty estimator is designed to estimate the uncertain dynamics and an adaptive parameter adjustment law is designed to estimate the actuator failure coefficients. Stability analysis and simulation results can demonstrate the effectiveness of the proposed method.

This paper presents a method of continuous-time simple-adaptive control (SAC) for multi-input multi-output (MIMO) nonlinear systems using multifraction neural networks. The control input is given by the sum of the output of the simple adaptive controller and the output of the multifraction neural network is used to compensate the nonlinearity of plant dynamics that is not taken into consideration in the usual SAC. The role of the multifraction neural network is to construct a linearized model by minimizing the output error caused by nonlinearities in the control systems.

This paper provides an inverse-model-based iterative learning control (ILC) for the unknown multi-input multi-output (MIMO) nonlinear system with neural network (NN), where a novel gradient adaptive law is used to update the NN weights both hidden and output layers such a faster convergence can be achieved. First, a three-layer NN structure is introduced to observe the MIMO nonlinear system with input–output data, and a new gradient algorithm is proposed to update the unknown parameters of both hidden and output layers. Then, the input dynamic can be obtained with the NN observer, and the inversion-model-based control is designed. Moreover, the ideal inversion control can be obtained based on the reference signal, and the inverse ILC is designed. The stability of the NN observer and the convergence of the inverse-model-based control are analyzed. Finally, a SCARA manipulator MIMO model is simulated to illustrate the correctness of the proposed methods.

A robust controller is developed for a class of multi-input multi-output (MIMO) uncertain nonlinear systems for which the robust backstepping method may not be applicable directly. The new design employs robust backstepping and forwarding construction of a Lyapunov function.

In this paper, an adaptive neural networks control approach is proposed for a class of multi-input multi-output (MIMO) non-affine nonlinear dynamic systems in the presence of input saturation. The difficulty in controlling the saturated non-affine system is overcome by introducing a system transformation, so as the system can be reformulated as an affine of a canonical system. In the control design, neural networks are used in the online learning of the unknown dynamics and the input saturation is approximated to reduce the influence caused by the nonlinearities, and a robustifying control term is used to compensate for the approximation errors. Compared to the literature, in the proposed approach, the structure of the designed controller is much simpler since the causes for the problem of complexity growing in existing methods are eliminated. The stability analysis of the closed-loop system is investigated by using Lyapunov theory. Numerical simulation illustrated the proposed control scheme with satisfactory results.

A traction force controller for passenger cars is presented in this paper to solve, in particular, the problem of guaranteeing the satisfaction of the fastest stable acceleration/deceleration conditions during vehicle operations. This problem is, for instance, an important subtask in the design of Intelligent vehicles/highways systems (IVHS), but it can be considered crucial also for any kind of modern medium to high-performance commercial cars. Due to system uncertainties, time-varying road conditions, and the wide range of operating conditions, which are typical of the automotive context, a robust control technique is required to solve this problem. The robust control methodology adopted in this paper is the so-called second order sliding mode control, which results particularly suitable to deal with uncertain nonlinear time-varying systems. Moreover, in contrast to conventional sliding mode control, second order sliding mode control generates continuous control actions, the discontinuities being confined to the derivatives of the control signals, thus resulting particularly suitable to be applied to automotive systems where vibrations suppression is a crucial requirement.

Block synchronization is a prerequisite to data-dependent superimposed training (DDST) based channel estimation. Mainly designed for single input single output (SISO) system, the existing block synchronization algorithms can hardly work for multi-input multi-output (MIMO) system. A new joint block synchronization, channel and dc-offset estimation algorithm based on balanced zero correlation zone (ZCZ) sequence for MIMO system is proposed in this paper. Analysis and simulation results show that the new algorithm has the same performance for SISO systems as the existing algorithms when their block and cyclic prefix lengths are the same. While for MIMO systems, the performance of the proposed algorithm is much better than that of the existing algorithms.

This article focuses on adaptive finite time control of multi-input multi-output (MIMO) nonlinear systems under time-varying actuator failures.A finite time adaptive control policy is proposed, guaranteeing the practical finite-time stability of the MIMO nonlinear systems with actuator failures. Simulation study illustrates the usefulness of the proposed policy.

최근 대용량, 초고속 통신 서비스의 비중이 높아짐에 따라 배열 안테나를 사용하는 MIMO(Multi-Input Multi-Output) 시스템의 활용이 중요하게 평가되고 있다. 하지만 기존의 MIMO 시스템은 다수의 안테나를 사용하기 때문에 안테나의 개수만큼 RF(Radio Frequency) 체인이 요구되며, 이로 인해 복잡도와 전력 소모가 크다는 단점을 가진다. 이러한 기존 MIMO 시스템의 단점을 해결하기 위해서 단일 능동 소자와 다수의 기생 소자를 이용하는 방식의 ESPAR(Electronically Steerable Parasitic Array Radiator) 안테나를 사용하는 빔 공간 MIMO 시스템에 대한 연구가 활발히 진행되고 있다. ESPAR 안테나를 사용하는 빔 공간 MIMO 시스템은 단일 RF 체인으로 구성되어 있기 때문에 기존 MIMO 시스템의 단점을 해결할 수 있다. 본 논문에서는 시스템의 보안성을 향상시키기 위해 QPSK(Quadrature Phase Shift Keying) 변조 방식의 ESPAR 안테나를 사용하는 빔 공간 MIMO 시스템에 비예측성, 비주기성, 구현의 용이성, 민감한 초기조건 등의 특징을 가지고 있는 카오스 통신 알고리즘을 적용하여 QPSK 변조 방식의 ESPAR 안테나를 사용하는 카오스 빔 공간 MIMO 시스템을 구성하고 성능을 평가한다. Recently, utilization of MIMO(Multi-Input Multi-Output) system using array antennas is evaluated significantly according to the extension of high-capacity and high-speed communication services. However, MIMO system has disadvantages such as high-complexity and high-power-consumption, because RF(Radio Frequency) chain is required as antenna number, and several array antenna is used in conventional MIMO system. In order to solve these problems, research about beamspace MIMO system using ESPAR(Electronically Steerable Parasitic Array Radiator) antenna that has single RF chain by using one active antenna and several parasitic elements has been studied actively. Beamspace MIMO system using ESPAR antenna is possible to solve the problems of conventional MIMO system, because this system is composed by single RF chain. In this paper, in order to improve the system security, chaos communication algorithm that has characteristics such as non-periodic, non-predictability, easy implementation and initial condition is applied to QPSK (Quadrature Phase Shift Keying) modulated beamspace MIMO system. We design the chaos QPSK modulated beamspace MIMO system, and evaluate SER performance of this system.

In wireless communication, multiple signals are utilized to receive and send information in the form of signals simultaneously. These signals consume little power and are usually inexpensive, with a high data rate during data transmission. An Multi Input Multi Output (MIMO) system uses numerous antennas to enhance the functionality of the system. Moreover, system intricacy and power utilization are difficult and highly complicated tasks to achieve in an Analog to Digital Converter (ADC) at the receiver side. An infinite number of MIMO channels are used in wireless networks to improve efficiency with Cross Entropy Optimization (CEO). ADC is a serious issue because the data of the accepted signal are completely lost. ADC is used in the MIMO channels to overcome the above issues, but it is very hard to implement and design. So, an efficient way to enhance the estimation of channels in the MIMO system is proposed in this paper with the utilization of the heuristic-based optimization technique. The main task of the implemented channel prediction framework is to predict the channel coefficient of the MIMO system at the transmitter side based on the receiver side error ratio, which is obtained from feedback information using a Hybrid Serial Cascaded Network (HSCN). Then, this multi-scaled cascaded autoencoder is combined with Long Short Term Memory (LSTM) with an attention mechanism. The parameters in the developed Hybrid Serial Cascaded Multi-scale Autoencoder and Attention LSTM are optimized using the developed Hybrid Revised Position-based Wild Horse and Energy Valley Optimizer (RP-WHEVO) algorithm for minimizing the "Root Mean Square Error (RMSE), Bit Error Rate (BER) and Mean Square Error (MSE)" of the estimated channel. Various experiments were carried out to analyze the accomplishment of the developed MIMO model. It was visible from the tests that the developed model enhanced the convergence rate and prediction performance along with a reduction in the computational costs.

Second order sliding mode controllers for altitude control of a quadrotor UAS: Real-time implementation in outdoor environments

In this article, an improved model-free adaptive control (iMFAC) is proposed for discrete-time multi-input multioutput (MIMO) nonlinear systems with an event-triggered transmission scheme and quantization (ETQ). First, an event-triggered scheme is designed, and the structure of the uniform quantizer with an encoding-decoding mechanism is given. With the concept of partial form dynamic linearization based on event-triggered and quantization (PFDL-ETQ), a linearized data model of the MIMO nonlinear system is constructed. Then, an improved model-free adaptive controller with the ETQ process is designed. By this design, the update of the pseudo partitioned Jacobean matrix (PPJM) estimates and control inputs occurs only when the trigger conditions are met, which reduces the network transmission burden and saves the computing resources. Theoretical analysis shows that the proposed iMFAC with the ETQ process can achieve a bounded convergence of tracking error. Finally, a numerical simulation and a biaxial gantry motor contour tracking control system simulation are given to illustrate the feasibility of the proposed iMFAC method with the ETQ process.