Unmatched Uncertainties Research Articles

Constrained Integrated Guidance and Control Scheme for Strap-Down Hypersonic Flight Vehicles with Partial Measurement and Unmatched Uncertainties

This paper investigates the issue of integrated guidance and control (IGC) design for strap-down hypersonic flight vehicles with partial measurement information and unmatched uncertainties. A constrained IGC scheme is proposed by combining the barrier Lyapunov function-based backstepping methodology and the specific output-based finite-time disturbance observer. Different from the existing methods, which require the state information and matched disturbances, the main features of the presented approach is capable of addressing the partial measurement knowledge and unmatched uncertainties simultaneously. The IGC model of hypersonic flight vehicles is first formulated, and based on that, the specific output-based finite-time disturbance observer (OFTDO) is proposed to achieve the finite-time estimation of the unmatched uncertainties through the output. Then, the constrained IGC strategy is constructed via the backstepping technique. The stability of the closed-loop system including the estimation and tracking errors dynamics is analyzed in detail. The effectiveness of the proposed method is verified by numerical simulations and Monte-Carlo tests.

Uncertainty Compensator and Fault Estimator-Based Exponential Supertwisting Sliding-Mode Controller for a Mobile Robot.

This work proposes a novel event-triggered exponential supertwisting algorithm (ESTA) for path tracking of a mobile robot. The proposed work is divided into three parts. In the first part, a fractional-order sliding surface-based exponential supertwisting event-triggered controller has been proposed. Fractional-order sliding surface improves the transient response, and the exponential supertwisting reaching law reduces the reaching phase time and eliminates the chattering. The event-triggering condition is derived using the Lipschitz method for minimum actuator utilization, and the interexecution time between two events is derived. In the second part, a fault estimator is designed to estimate the actuator fault using the Lyapunov stability theory. Furthermore, it is shown that in the presence of matched and unmatched uncertainty, event-trigger-based controller performance degrades. Hence, in the third part, an integral sliding-mode controller (ISMC) has been clubbed with the event-trigger ESTA for filtering of the uncertainties. It is also shown that when fault estimator-based ESTA is clubbed with ISMC, then the robustness of the controller increases, and the tracking performance improves. This novel technique is robust toward uncertainty and fault, offers finite-time convergence, reduces chattering, and offers minimum resource utilization. Simulations and experimental studies are carried out to validate the advantages of the proposed controller over the existing methods.

H∞ Codesign for Uncertain Nonlinear Control Systems Based on Policy Iteration Method.

In this article, the problem of H∞ codesign for nonlinear control systems with unmatched uncertainties and adjustable parameters is investigated. The main purpose is to solve the adjustable parameters and H∞ controller simultaneously so that better robust control performance can be achieved. By introducing a bounded function and defining a special cost function, the problem of solving the Hamilton-Jacobi-Isaacs equation is transformed into an optimization problem with nonlinear inequality constraints. Based on the sum of squares technique, a novel policy iteration algorithm is proposed to solve the problem of the H∞ codesign. Moreover, one modified algorithm for optimizing the robust performance index is given. The convergence and the performance improvement of new iteration policy algorithms are proved. Simulation results are presented to demonstrate the effectiveness of the proposed algorithms.

Robust control design for rotary inverted pendulum with unmatched uncertainty

Robust control design for rotary inverted pendulum with unmatched uncertainty

Threshold design for fault detection with first order sliding mode observers

Sliding Mode Observer (SMO) based methods have been extensively used for Fault Estimation (FE). However, the fault detection (FD) problem for these SMO based FE methods has not been completely solved. In this paper a robust threshold on the so-called Equivalent Output Injection (EOI) is presented which enables FD for systems with measurement noise and unmatched uncertainties. This threshold is applicable to a large class of existing SMO based FE methods, and its applicability can easily be verified. Theoretical guarantees on the detection performance of this threshold are provided, and further demonstrated via a simulation study.

Decentralised output tracking of interconnected systems with unknown interconnections using sliding mode control

In this paper, a class of nonlinear interconnected systems with matched and unmatched uncertainties is considered. The isolated subsystem dynamics are described by linear systems with nonlinear components. The matched uncertainties and unmatched unknown interconnection terms are assumed to be bounded by known nonlinear functions. Based on sliding mode techniques, a state feedback decentralised control scheme is proposed such that the outputs of the controlled interconnected system track given desired signals uniformly ultimately. The desired reference signals are allowed to be time-varying. Using appropriate transformations, the considered system is transformed into a new interconnected system with an appropriate structure to facilitate the sliding surface design and the decentralised control design. A set of conditions is proposed to guarantee that the designed controller drives the tracking errors onto the sliding surface. The sliding motion exhibited by the error dynamics is uniformly ultimately bounded. The developed results are applied to a river quality control problem. Simulation results show that the proposed decentralised control strategy is effective and feasible.

Proportional-Integral Event-Triggered Control of Networked Systems With Unmatched Uncertainties

This article proposes a proportional-integral (PI) event-triggered control strategy for networked nonlinear systems subject to unmatched uncertainties. The influences of the unmatched uncertainties and external disturbances on the output channel are attenuated by an extended-state-observer-based output feedback controller through a state transformation. The outputs of the controller are transmitted in an event-triggered fashion by comparing the difference between the current sampling error and its integration with respect to time. We prove the stability of the closed-loop event-triggered control system by regulating the trajectories of the observation and tracking errors into a compact set. Further, the relationships between the control performance and designed parameters are investigated quantitatively. In addition, Zeno-freeness is guaranteed by proving the existence of a nonzero minimum inter-event time. Finally, the effectiveness of the proposed PI-type event-triggered control strategy in reducing signal transmission rate is validated through numerical examples and various experiments.

Funnel asymptotic tracking of nonlinear multi-agent systems with unmatched uncertainties

This work investigates the asymptotic consensus tracking for high-order uncertain nonlinear multi-agent systems (MASs), in the presence of pre-specified funnel constraints, unmatched uncertainties and possibly discontinuous dynamics. A new distributed discontinuous funnel controller is constructed to ensure asymptotic convergence of the consensus errors with satisfaction of the funnel boundary. The controller is analyzed using non-smooth analysis. The presented solution extends funnel control results proposed in the literature beyond the matched uncertainties and the first/second-order dynamics cases. A numerical study finally illustrates the method.

Active disturbance rejection adaptive control of multi‐degrees of freedom hydraulic manipulators

SummaryThis article investigates the precise motion control of multi‐degrees of freedom (DoF) hydraulic manipulators, and proposes an active disturbance rejection adaptive control (ADRAC) architecture based on full state feedback with consideration of both unmatched and matched uncertainties, that is, parametric uncertainties and uncertain nonlinearities. The new control strategy integrates adaptive control with extended state observer (ESO) via the backstepping method. Parametric uncertainties are handled by the synthesized adaptive law, and ESO is designed to estimate the remaining uncertainties before being compensated in a feedforward way. In particular, the unmatched and matched uncertainties can be observed in real‐time by constructing an ESO for each channel of the hydraulic manipulator system. The burden on ESO should be greatly reduced since parameter adaptation offsets most parametric uncertainties. Accordingly, high‐gain feedback is avoided in the resulting controller, and improved servo performance can thus be expected. In theory, the suggested ADRAC controller can attain asymptotic tracking performance under the influence of not only parametric uncertainties derived from various hydraulic parameters but also invariant disturbances. Furthermore, when uncertain nonlinearities become time‐variant, prescribed transient tracking performance and final tracking accuracy can also be ensured. Comparative simulations concerning both matched and unmatched uncertainties are obtained to illustrate the high tracking performance nature of the developed control algorithm.

Fault-Tolerant Control of Linear Systems with Unmatched Uncertainties Based on Integral Sliding Mode Technique

This paper proposes a novel fault-tolerant control method based on the integral sliding mode technique for unmatched uncertain linear systems with external perturbations. Differently from the existing works, the uncertainties under consideration have an unmatched norm-bounded form in the system and input matrix. Based on linear matrix inequalities, the existence conditions of the sliding mode surface are presented. The unknown fault information is then estimated by some adaptive laws. On the grounds of that, an integral sliding mode controller is also obtained to guarantee the disturbance attenuation and fault tolerance for linear uncertain systems with unmatched uncertainties and actuator faults from the initial time. Finally, the comparative simulation results verify the effectiveness of our presented scheme.

A Modified Active-Disturbance-Rejection Control with Sliding Modes for an Uncertain System by Using a Novel Reaching Law

This article presents a modified active-disturbance-rejection control (ADRC) combined with a sliding mode control (SMC) regarding the tracking control problems for plants with unmatched uncertainty. The proposed modified active-disturbance-rejection control with sliding mode (ADRC-SM) employs a reduced-order extended state observer (ESO) for estimating various uncertainties of system in time, including unmatched and matched uncertainties. Meanwhile, a novel reaching law of SMC was designed by using the cycloid function as the main controller of ADRC, which ensures the robustness of the uncertain system. Due to the reduced-order ESO tracking and compensating for various uncertainties in the system as a total disturbance, the upper bound of the disturbance in the SMC is relaxed. The gain coefficient of the reaching law only needs to be designed to be larger than the limit of the lumped disturbance; thus, the chattering problem is greatly reduced. The designed new reaching law of the cycloid function shortens the time for the system state’s convergence to the sliding mode’s surface. The cycloid function replaces the switching function in the traditional reaching law, making the actual control input continuous and shortening the approach time. Compared with traditional ADRC-SM, the use of multiple ESOs or intelligent algorithms to approximate plant parameters can be avoided, the design is simplified, its robustness is enhanced, computational costs are reduced, and the convergence time is reduced. The controlled object with unmatched uncertainty is transformed into a system with matched uncertainty using state-space transformation, which reduces the complexity of the controller’s design. In addition, the stability analysis of the closed-loop system is carried out based on the Lyapunov method. Simulations and experiments verify that the modified ADRC-SM has the merits of fast response, small overshoot, small steady-state error, strong anti-interference competence, and high control accuracy.

Full-Order Terminal Sliding-Mode Control for Soft Open Point

In this paper, a full-order terminal sliding-mode control method is proposed for the rectifier side and the inverter side of the soft open point (SOP). The rectifier-side DC voltage control system consists of the voltage- and current-loops with controllers which are designed using full-order sliding-mode (FOSM) to enhance the dynamic performances and anti-disturbance. The integral type virtual control signal without chattering is designed to compensate for the unmatched uncertainties including external disturbances and some parameter perturbations. The full-order terminal sliding-mode (FOTSM) controller for the current-loop can force the current response to track its reference in finite time. The inverter side power control system is designed to regulate the power. The FOTSM controller for the power-loop ensures the power-tracking accuracy under a disturbed condition. Finally, the simulations demonstrate the effectiveness of the proposed controllers for the rectifier and inverter sides in the soft open point (SOP).

Cross backstepping sliding mode control using integral barrier Lyapunov function for cross‐strict feedback systems

Cross-backstepping control for a type of uncertain non-strict-feedback non-linear systems with time-varying partial state constraints is the main subject of this work. Non-strict-feedback non-linear systems are partitioned into two strict-feedback non-linear subsystems: constrained subsystem and unconstrained subsystem. An integral barrier Lyapunov function (IBLF) is used in each step of the backstepping design for the constrained subsystem to guarantee the boundedness of the fictional or actual state tracking errors. The effect of uncertainty is reduced using a hybrid cross-backstepping sliding mode control (SMC) technique. The algorithm employs a systematic approach to developing control laws for non-linear systems with matched and unmatched uncertainties. The simulation results of the proposed controller are juxtaposed with those of the cross backstepping with the time-varying barrier Lyapunov function (TVBLF). The results demonstrate the overall better performance of the proposed method.

Adaptive control of nonlinear plant with unmatched parametric uncertainties and input saturation

The problem of adaptive control of a parametrically uncertain nonlinear plant presented in a state-feedback form with unmatched uncertainties and input constraint is considered. The solution is based on adaptive backstepping procedure, in which the virtual controls includes the high-order time derivatives of adjustable parameters calculated with the use of an adaptation algorithm with improved parametric convergence. Analytical design of control with compensation for the influence of input constraints is performed using of a special filter. The approach presented in this paper allows one to design an adaptive controller that ensures the boundedness for all signals in the closed-loop system and provides tracking of the reference signal. Simulation results presented in the MATLAB/Simulink environment illustrate the performance of the presented approach and the acceleration of parametric convergence with an increase of the adaptation coefficient. The plant considered in this work describes a wide class of systems, such as various manipulation robots, technological processes, electromagnetic levitation systems, chemical processes, etc. The proposed control algorithm considers natural for practical applications input constraints and significantly reduces the influence of the regulator parameters tuning speed on the control system transient processes.

Global Iterative Sliding Mode Control of an Industrial Biaxial Gantry System for Contouring Motion Tasks

This paper proposes a global iterative sliding mode control approach for high-precision contouring tasks of a flexure-linked biaxial gantry system. For such high-precision contouring tasks, it is the typical situation that the involved multi-axis cooperation is one of the most challenging problems. As also would be inevitably encountered, various factors render the multi-axis cooperation rather difficult; such as the strong coupling (which naturally brings nonlinearity) between different axes due to its mechanical structure, the backlash and deadzone caused by the friction, and the difficulties in system identification, etc. To overcome the above-mentioned issues, this work investigates an intelligent model-free contouring control method for such a multi-axis motion stage. Essentially in the methodology developed here, it is firstly ensured that all the coupling, friction, nonlinearity, and disturbance (regarded as uncertain dynamics in each axis) are suitably posed as `uncertainties'. Then, a varying-gain sliding mode control method is proposed to adaptively compensate for the matched unknown dynamics in the time domain, while an iterative learning law is applied to suppress the undesirable effects (arising from the repetitive matched and unmatched uncertainties in the iteration domain). With this approach, the chattering that typically results from the overestimated control gains in the sliding mode control is thus suppressed during the iterations. To analyze the contouring performance and show the improved outcomes, rigorous proof is furnished on both the stability in the time domain and the convergence in the iteration domain; and the real-time experiments also illustrate that the requirements of precision motion control towards high-speed and complex-curvature references can be satisfied using the proposed method, without prior knowledge of the boundary to the unknown dynamics.

Adaptive Memoryless Sliding Mode Control of Uncertain Rössler Systems with Unknown Time Delays

In this paper, by adopting sliding mode control, an adaptive memoryless control scheme has been developed for uncertain Rössler chaotic systems with unknown time delays. Firstly, the proposed adaptive control can force the trajectories of controlled Rössler time-delayed chaotic systems into the specified sliding manifold. Then, the Riemann sum is introduced to analyze the stability of the equivalent dynamics in the sliding manifold. The control performance can be predicted even if the controlled systems have unmatched uncertainties and unknown time delays, which have not been well addressed in the literature. Numerical simulations are included to demonstrate the feasibility of the proposed scheme.

Robust chaos suppression of uncertain unified chaotic systems based on chattering-free sliding mode control

For continuous sliding mode control (SMC) in the unified chaotic systems subjected to matched/unmatched uncertainties, a novel chattering-free SMC design is proposed. First, an augmented state is introduced such that it becomes possible to develop a continuous controller to eliminate the undesired chattering which often appears in the typical SMC. Then by using this chattering-free controller, the chaos behavior in unified chaotic systems with matched uncertainties can be completely suppressed. As for the unmatched uncertainties, every state of controlled systems can be driven and limited to a predictable bound, which is not addressed in the literature. Finally, the effectiveness of the proposed chattering-free controller is verified by the numerical simulations.

Generalized proportional integral observer‐based event‐triggered control for frequency regulation in power systems with wind energy

AbstractThe article addresses a generalized proportional–integral observer (GPIO)‐based event‐triggered control (ETC) for load frequency problems in power systems with wind energy integration. The concept of static event‐triggered mechanism (ETM) with a fixed threshold parameter may be unreasonable in some engineering applications where the transmission rates are time varying as in the case with power systems. Therefore, in this work, a dynamic ETM is designed to dynamically adjust the threshold parameters over time to reflect the time‐varying transmission rates. The unmatched uncertainties are suppressed via high‐gain design while the external disturbance (wind speed) is estimated and attenuated by the GPIO‐based ETC. The proposed design ensures frequency and tie‐line power stabilization and saves the computational and communication resources more effectively than recently reported works in the field. The hybrid closed‐loop system's global bounded stability is theoretically proved and verified by simulation in three‐area interconnected power systems.

L1 adaptive output-feedback fault-tolerant control for uncertain nonlinear systems subject to unmodeled actuator dynamics and faults

This paper develops a L1 adaptive output-feedback fault-tolerant controller for uncertain nonlinear systems in the presence of unmodeled actuator dynamics and actuator faults. The proposed controller consists of the output predictor, adaptive laws, and the control law. The output predictor is a dynamic system expressed as a linear system with adaptive parameters which mean the matched uncertainties and the unmatched uncertainties. Piecewise-constant adaptive laws are designed to update the adaptive parameters so that the estimation error is driven to zero at each integration time step. The control law with low-pass filters is introduced to compensate for the performance degradation because of system uncertainties, unmodeled actuator dynamics and faults, and to guarantee the uniform boundedness of the input and output signals of the system. Two simulation examples verify the effectiveness of the proposed controller.

New Results on the Generalized Discrete Reaching Law With Positive or Negative Decay Factors

Dynamic characteristics of sliding variables for the generalized discrete reaching law are investigated, such as phenomena of reaching condition and ultimate boundedness of sliding variables. The discussed reaching law is relatively more general than some others in the literature, because it contains a wider range of decay factors, which could be positive or negative. First, a sufficient and necessary condition is obtained ensuring that the generalized reaching law satisfies the reaching condition. Then, the dependence between the ultimate bounding of sliding variables (i.e., the range of steady-state chattering) and parameters in the generalized reaching law is discussed. The discussions are stated in three different cases, i.e., negative decay factors, adjustable negative decay factors, and adjustable positive decay factors. The obtained results of the generalized reaching law are further applied to the discrete control system with unmatched uncertainties to demonstrate the usefulness of this generalized discrete reaching law in sliding-mode control theory. Finally, two simulation examples are given to illustrate the validity of our findings.