Adaptive sliding mode control for a class of MIMO nonlinear systems with uncertainties

This paper proposes an adaptive scheme of designing sliding mode control (SMC) for affine class of multi-input multi-output (MIMO) nonlinear systems with uncertainty in the systems dynamics and control distribution gain. The proposed adaptive SMC does not require any a priori knowledge of the uncertainty bounds and therefore offers significant advantages over the non-adaptive schemes of SMC design. The closed loop stability conditions are derived based on Lyapunov theory. The effectiveness of the proposed approach is demonstrated via simulations considering an example of a two-link robot manipulator and has been found to be satisfactory.     

Robust finite-time cooperative formation control of UGV-UAV with model uncertainties and actuator faults

This paper investigates the finite-time cooperative formation control problem for a heterogeneous system consisting of an unmanned ground vehicle (UGV) - the leader and an unmanned aerial vehicle (UAV) - the follower. The UAV system under consideration is subject to modeling uncertainties, external disturbance as well as actuator faults simultaneously, which is associated with aerodynamic and gyroscopic effects, payload mass, and other external forces. First, a backstepping controller is developed to stabilize the leader system to track the desired trajectory. Second, a robust nonsingular fast terminal sliding mode surface is designed for UAV and finite-time position control is achieved using terminal sliding mode technique, which ensures the formation error converges to zero in finite time in the presence of actuator faults and other uncertainties. Furthermore, by combining the radial basis function neural networks (NNs) with adaptive virtual parameter technology, a novel NN-based adaptive nonsingular fast terminal sliding formation controller (NN-ANFTSMFC) is developed. By means of the proposed adaptive control strategy, both uncertainties and actuator faults can be compensated without the prior knowledges of the uncertainty bounds and fault information. By using the proposed control schemes, larger actuator faults can be tolerated while eliminating control chattering. In order to realize fast coordinated formation, the expected position trajectory of UAV is composed of the leader position information and the desired relative distance with UGV, based on local distributed theory, in the three-dimensional space. The tracking and formation controllers are proved to be stable by the Lyapunov theory and the simulation results demonstrate the effectiveness of proposed algorithms.     

Launch vehicle attitude control using sliding mode control and observation techniques

In determining flight controls for launch vehicle systems, several uncertain factors must be taken into account, including a variety of payloads, a wide range of flight conditions and different mission profiles, wind disturbances and plant uncertainties. Crewed vehicles must adhere to human rating requirements, which limit the angular rates. Sliding mode control algorithms that are inherently robust to external disturbances and plant uncertainties are very good candidates for improving the robustness and accuracy of the flight control systems. Recently emerging Higher Order Sliding Mode (HOSM) control is even more powerful than the classical Sliding Mode Controls (SMC), including the capability to handle systems with arbitrary relative degree. This paper proposes sliding mode launch vehicle flight controls using classical SMC driven by the sliding mode disturbance observer (SMDO) and higher-order multiple and single loop designs. A case study on the SLV-X Launch Vehicle studied under a joint DARPA/Air Force program called the Force Application and Launch from CONtinental United States (FALCON) program is shown. The intensive simulations demonstrate efficacy of the proposed HOSM and SMC-SMDO control algorithms for launch vehicle attitude control.     

Observer-based discrete-time sliding mode control for systems with unmatched uncertainties

This paper addresses an observer-based sliding mode control (SMC) approach for discrete-time systems with unmatched uncertainties. A modified sliding surface based on disturbance estimation and a sliding mode controller are designed to counteract with the unmatched disturbance. The proposed method exhibits the following three features. First, the hyperplane matrix is designed in a simple way based on the discrete-time Riccati equation. Second, a chattering-free SMC method is utilized. Third, the proposed approach retains the nominal performance of the system. The stability of the overall system is achieved and simulation results are presented to verify the effectiveness of the proposed method.     

A multi input sliding mode control for Peltier Cells using a cold–hot sliding surface

This paper deals with an application of the Sliding Mode Control (SMC) in the presence of lumped temperature disturbances in Peltier Cells (PCs). A controller is proposed so that a temperature disturbance reduction is obtained. A constructive Theorem based on a particular sliding mode surface using Lyapunov approach is demonstrated. Specifically, the proven Theorem shows a structural control law which consists of an interacting input law between the two available inputs of current and forced heat convection transfer function (ventilation input). The sliding mode surface is defined in terms of cold and hot state variables, emphasizing a new two sided control approach for PCs. In terms of applications, the localization problems are very important to minimize errors in all cases in which PCs are used. The application approach is targeted on a novel workpiece clamping device, which uses PCs to freeze water on a metallic plate under subzero temperatures. The ice structure is capable of evolving enough bonding strength to clamp workpieces form and force-fitted during machining operations without deforming the piece mechanically. This capability is especially crucial for micro parts as well as for hard to clamp pieces made of brittle or soft materials and irregular shaped complex geometries. The proposed SMC approach shows a robustness against the parametric uncertainties due to the nonlinear model of PCs. Computer simulation results as well as measurements are shown.     

Design of adaptive sliding mode controller for robust tracking and model following

The problem of the robust tracking and model following for a class of linear systems with time-varying parameter uncertainties, multiple delayed state perturbations and external disturbance is investigated in this paper. The algorithm is based on the adaptive sliding mode control. The proposed method does not need a priori knowledge of upper bounds on the norm of the uncertainties, but estimates them by using the adaptation technique so that the reaching condition can be satisfied. This scheme guarantees the closed-loop system stability and zero-tracking error in the presence of time-varying parameter uncertainties, multiple delayed state perturbations and external disturbance. Finally, simulation results demonstrate the efficacy of the proposed control methodology.     

Algorithms for chattering reduction in system control

Sliding mode control (SMC) is among the popular approaches for control of systems, especially for unknown nonlinear systems. However, the chattering in SMC is generally a problem that needs to be resolved for better control. A time-varying method is proposed for determining the sliding gain function in the SMC. Two alternative tuning algorithms are proposed for reducing the sliding gain function for systems. The first algorithm is for systems with no noise and disturbance but with or without unmodeled dynamics. The second algorithm is for systems with noise, disturbance, unmodeled dynamics, or any combination of them. Compared with the state-dependent, equivalent-control-dependent, and hysteresis loop methods, the proposed algorithms are more straightforward and easy to implement. The performance of the algorithms is evaluated for five different cases. A 90% to 95% reduction of chattering is achieved for the first algorithm used for systems with sensor dynamics only. By using the second algorithm, the chattering is reduced by 70% to 90% for systems with noise and/or disturbance, and by 25% to 50% for systems with a combination of disturbance, noise, and unmodeled dynamics.     

On novel trajectory tracking control of quadrotor UAV: A finite-time guaranteed performance approach

In this work, aiming at the trajectory tracking control of the quadrotor UAV subject to external disturbances and model uncertainties, a finite-time approach with preassigned performance guaranteed is proposed. First, the control system is decoupled into translational and rotational subsystems. Then, in both two subsystems, the performance bounds constructed by the newly established appointed-time performance functions are devised for guaranteeing the tracking performance, and the controllers are designed via applying the dynamic surface control technique with integral barrier Lyapunov functions involved. Moreover, finite-time tracking differentiators and finite-time multivariable disturbance observers are exploited to estimate the target signals and the lumped disturbances, respectively. Finally, two examples of simulation are carried out to validate the effectiveness and superiority of the proposed control method.     

Sliding mode control design using generalized relative degree approach: Aerospace application

Relative degree (RD) approach is a powerful tool for obtaining system's input-output dynamics used for output tracking controller designs of minimum phase systems. Designs using the RD alone can fail due both to insufficient control authority in minimum phase systems, and instability of internal/zero dynamics attributed to nonminimum phase systems. A novel definition and a concept of Practical Generalized RD (PGRD) are proposed in this paper and are used in concert with Sliding Mode Control (SMC) to compensate for system perturbations in minimum phase systems. The use of known Generalized Relative Degree (GRD) in nonminimum phase systems allows for the elimination of internal dynamics. However, instability that emerges in the corresponding control dynamic extension is defeating any output tracking controller design. A novel methodology of using GRD for designing continuous SMC in nonminimum phase systems is presented. An algorithm for generating a bounded solution of the unstable dynamic extension is proposed and used in concert with SMC, allowing robust control design for nonminimum phase systems. The efficacy of the proposed GRD-based approaches is demonstrated on a minimum and nonminimum phase rocket attitude control problem both analytically and via simulation.     

Passivity-based adaptive tracking control of spacecraft line-of-sight relative motion with thrust saturation

This paper considers the control problem of spacecraft line-of-sight (LOS) relative motion with thrust saturation in the presence of unmodeled dynamics, external disturbance and unknown mass property. By using skew-symmetric property, reference trajectory generator and anti-windup technique, a novel passivity-based adaptive sliding mode control (SMC) scheme is proposed without prior knowledge of uncertainty/disturbance bound. Within the Lyapunov framework, the establishment of a real sliding mode (which induces the practical stability of closed-loop error system) is validated. The main contributions are that a new control gain adaptive algorithm is adopted to attenuate the overestimation of switching gain and a differentiable projection-based parameter adaptive algorithm is proposed to force the mass approximator to remain in a desired domain, then the adaptive control law is modified by the reference trajectory generator and anti-windup technique to compensate for the effect of thrust saturation. Finally, simulations are conducted to show the fine performance of proposed control scheme.     

Distributed event-triggered sliding mode control of switched systems

This paper investigates the problem of distributed event-triggered sliding mode control (SMC) for switched systems with limited communication capacity. Moreover, the system output and switching signals are both considered to be sampled by distributed digital sensors, which may cause control delay and asynchronous switching. First of all, a novel distributed event-triggering scheme for switched systems is proposed to reduce bandwidth requirements. Then, a state observer is designed to estimate the system state via sampled system output with transmission delay. Based on the observed system state, a switched SMC law and corresponding switching law are designed to guarantee the exponential stability of the closed-loop system with H_∞ performance. Finally, an application example is given to illustrate the effectiveness of the proposed method.     

Integral sliding-mode fixed-time consensus tracking for second-order non-linear and time delay multi-agent systems

In this paper, fixed-time consensus tracking problems under directed interaction topologies for second-order non-linear multi-agent systems with disturbance and second-order multi-agent systems with input delay are investigated. Two continuous integral terminal sliding modes are designed, which can effectively eliminate the singularity and chattering. Correspondingly, two fixed-time distributed control protocols are proposed based on the designed continuous ITSM to ensure that the consensus tracking are achieved in fixed-time. It is shown that the upper bounds of settling time are regardless of initial conditions. The rigorous proofs are given by employing Lyapunov stability theory and fixed-time stability theory. Simulations are provided to verify the effectiveness of the theoretical results.     

Adaptive second order terminal sliding mode controller for robotic manipulators

In this paper an adaptive second order terminal sliding mode (SOTSM) controller is proposed for controlling robotic manipulators. Instead of the normal control input, its time derivative is used in the proposed controller. The discontinuous sign function is contained in the derivative control and the actual control obtained after integration is continuous and hence chatterless. An adaptive tuning method is utilized to deal with the system uncertainties whose upper bounds are not required to be known in advance. The performance of the proposed control strategy is evaluated through the control of a two-link rigid robotic manipulator. Simulation results demonstrate the effectiveness of the proposed control method.     

Optimization of air–fuel ratio control of fuel-powered UAV engine using adaptive fuzzy-PID

Traditional control method of air–fuel ratio (AFR) of aero engine cannot meet the performance requirement of fuel-powered unmanned aerial vehicle (UAV), which may lead to efficiency reduction and emission increase. In order to improve the control accuracy, this paper proposes a new AFR control method based on fuzzy-PID. We analyze the control results under different working conditions by using adaptive fuzzy-PID. Through simulation and experimental studies, we can draw the conclusions as follows: compared with PID control method, firstly, AFR control error can be reduced by 80% in normal condition; secondly, the control error is reduced by 55% in rapid acceleration condition; in addition, the control error can be reduced by 71% in continuous disturbance condition; comparison results with existing Fuzzy-PID also show that the improved controller has advantage in terms of resisting rapid and continuous interferences; moreover, in practical application of fuzzy-PID control, the highest AFR errors are about 3%. In normal condition, the error is reduced from 5 to 1% compared with PID control, which demonstrates the effectiveness of the improved fuzzy-PID control model. This research can be a reference in the application of UAV aero engine control.     

H∞ guaranteed cost control for uncertain Markovian jump systems with mode-dependent distributed delays and input delays

This paper investigates the H_∞ guaranteed cost control problem for mode-dependent time-delay jump systems with norm-bounded uncertain parameters. Both distributed delays and input delays appear in the system model. Based on a matrix inequality, a sufficient condition for the existence of robust H_∞ guaranteed cost controller is derived, which stabilizes the considered system and guarantees that both the H_∞ performance level and a cost function have upper bounds for all admissible uncertainties. By the cone complementary linearization approach, the desired state-feedback controller can be constructed. A numerical example is provided to show the effectiveness of the proposed theoretical results.     

H∞ output-feedback control for discrete-time switched linear systems via asynchronous switching

In this paper, we consider the H_∞ hybrid dynamical output-feedback control problem for discrete-time switched linear systems under asynchronous switching. A time-varying multiple Lyapunov-like-function (MLF) approach is applied to derive sufficient conditions that guarantee the stability and weighted l₂-gain performance of the closed-loop systems, where the established conditions explicitly depend on the upper and lower bounds of asynchronous switching delays. An alternative approach is proposed to decouple the bilinear problems of the control synthesis conditions. Convex optimization algorithms are also proposed based on the established conditions to determine the minimum l₂-gain performance. Two numerical examples are provided to illustrate the effectiveness of the proposed method, demonstrating significant improvement over the existing results.     

NMPC-based UAV-USV cooperative tracking and landing

The study aims to solve the problem of real time tracking and precise landing of unmanned aerial vehicle (UAV) during unmanned surface vehicle (USV) navigation. In this paper, a UAV-USV cooperative tracking and landing control strategy based on nonlinear model predictive control (NMPC) is proposed. Firstly, the UAV-USV heterogeneous intelligent body collaborative system is constructed based on the mathematical model of UAV and USV; secondly, the tracking controller is designed based on NMPC algorithm to ensure that the UAV can track the USV in real time; finally, a UAV-USV cooperative landing control strategy is proposed to realize the heave motion of the USV to the peak vertex, thus, the UAV completes the precise landing with the minimum impact. As the simulation experimental results show, the UAV-USV cooperative tracking and landing control scheme proposed in this paper can provide effective solution against real time tracking and accurate landing of UAV during the navigation of USV.     

Adaptive fractional order sliding mode controller with neural estimator

In this study, an adaptive fractional order sliding mode controller with a neural estimator is proposed for a class of systems with nonlinear disturbances. Compared with traditional sliding mode controller, the new proposed fractional order sliding mode controller contains a fractional order term in the sliding surface. The fractional order sliding surface is used in adaptive laws which are derived in the framework of Lyapunov stability theory. The bound of the disturbances is estimated by a radial basis function neural network to relax the requirement of disturbance bound. To investigate the effectiveness of the proposed adaptive neural fractional order sliding mode controller, the methodology is applied to a Z-axis Micro-Electro-Mechanical System (MEMS) gyroscope to control the vibrating dynamics of the proof mass. Simulation results demonstrate that the proposed control system can improve tracking performance as well as parameter identification performance.     

Barrier function-based nonsingular prescribed performance terminal sliding mode tracker for under-actuated nonlinear systems: Experimental study

In this paper, an adaptive concave barrier function scheme coupled with the non-singular terminal sliding mode control technique is proposed for finite-time tracking control of the under-actuated nonlinear system in the existence of model uncertainty, external disturbance and input saturation. Firstly, the dynamical equation of under-actuated nonlinear n-order system is expressed under model uncertainty, external disturbance and input saturation. Secondly, for the improvement of stability performance of the system in the existence of input saturation, a compensation system is designed to overcome the constraint on the control input. Afterward, the tracking errors between actual states of the system and differentiable reference signals are defined and the sliding surface based on the defined tracking errors is presented. Then, for gaining the better transient and steady-state performance of the closed-loop system, the prescribed performance control scheme is adopted. Based on this method, the transformed prescribed form of the previous determined sliding surface is obtained to ensure that the sliding surface can reach to a predefined region. Afterward, for assurance of the finite-time reachability of transformed sliding surface, the nonsingular terminal sliding surface is recommended. In addition, for the compensation of the model uncertainty and external disturbance existed in the system, the adaptive-based concave barrier function technique is used to estimate the unknown bounds of uncertainty and exterior disturbance. Finally, for demonstration of the proposed control method, the simulations and experimental implementation are done on the air levitation system.     

Robust bounds for fractional-order systems with uncertain order and structured perturbations via Cylindrical Algebraic Decomposition method

This paper considers the robust stability problem of fractional-order systems with uncertain order and structured perturbations. A stability check procedure is proposed for determining the robust bounds of uncertain order and other uncertain parameters for fractional-order systems.The results are obtained in terms of Cylindrical Algebraic Decomposition which is first used for analyzing the robust stability problem of fractional-order systems with uncertain order. The method is non-conservative for fractional-order systems with the uncertain order α satisfying 0?<?α?<?2. Examples are given to demonstrate the effectiveness of proposed approach.