Unmatched Uncertainties Research Articles

Adaptive Door Opening Control Algorithm of Bio-Inspired Mobile Manipulator Based on Synchronous Sensing.

At present, the research of robot door opening method is basically realized by identifying the door handle through the synchronous sensing system on the premise that the bio-inspired mobile manipulator is located in front of the door. An adaptive door opening strategy of a bio-inspired mobile manipulator based on a synchronous sensing system is proposed. Firstly, the random delay distribution in clock synchronization technology is analyzed in detail, and its distribution is verified on the experimental platform of adjacent nodes. Based on the Gaussian distribution of random delay, the relative frequency offset and relative phase offset of adjacent nodes are calculated. The clock synchronization of network cable sensor nodes is realized. Secondly, based on the information data of synchronous sensing system, this article realizes target detection and tracking based on depth network. In addition, based on the sliding mode control theory, the dynamic model of the nonholonomic bio-inspired mobile manipulator is applied. Finally, a robust adaptive sliding mode control method for nonlinear systems with input gain uncertainty and unmatched uncertainty is proposed by combining adaptive backstepping with sliding mode control. By adding sliding mode control in the last step of adaptive backstepping, the uncertainty of the system is compensated, and the system trajectory is maintained on the specified sliding mode manifold. The tracking control and stability control of the nonholonomic bio-inspired mobile manipulator are simulated. The experimental and simulation results show that the control method proposed in this article is effective and feasible.

Immersion and invariance adaptive decentralized control for the speed and tension system of the reversible cold strip rolling mill

AbstractAn immersion and invariance (I&I) adaptive decentralized control strategy is proposed for the speed and tension system of the reversible cold strip rolling mill, which is characterized by multiple variable, nonlinearity, strong coupling effect, and uncertainty. First, a sliding mode observer (SMO) is constructed to estimate the unmatched uncertainty of the system to improve the tracking control precision. Second, the I&I theory‐based estimators are designed to estimate the perturbation parameters of the system, and the parameter estimation errors converge monotonically following an exponential law. Third, the I&I theory‐based decentralized controllers are designed for the speed and tension system of the reversible cold strip rolling mill, which achieve precise tracking controls for the given values of the system. Theoretical analysis shows that the resulting closed‐loop system is globally stable. Finally, the simulation research is carried out on the speed and tension system of a 1422 mm reversible cold strip rolling mill using actual data, and the simulation results verify the superiority of the proposed control strategy in comparison with the I&I control strategy and the backstepping dynamic surface control strategy.

Exponentially Convergent Direct Adaptive Pole Placement Control of Plants With Unmatched Uncertainty Under FE Condition

A new method of direct adaptive pole placement control (APPC) is developed for plants with unmatched uncertainty, which linearly depends on a state vector. It guarantees the exponential stability of a control system and exponential convergence of control law adjustable parameters to their true values when the regressor is finitely exciting. Considering the known classical APPC schemes and adaptive methods with exponential regulation, the advantages of the proposed one are that it does not require a priori information on a control input matrix and ensures the monotonic transient behavior of each adjustable parameter of the control law. The theoretical results are supported by the numerical experiments.

Adaptive Optimal Multi-Surface Back-Stepping Sliding Mode Control Design for the Takagi-Sugeno Fuzzy Model of Uncertain Nonlinear System With External Disturbance

This paper proposes a novel scheme of the multi-objective robust control design for a class of uncertain nonlinear systems in strict-feedback-form based on Takagi–Sugeno fuzzy model (TSFM). The nonlinear system contains both the matched and the unmatched uncertainties and also subjected to the external disturbances. The TSFM provides the generalization of the linear systems concepts to the nonlinear systems field in a convex framework. First, a new sliding surface is defined using a convex combination of the surfaces which are defined for each fuzzy rule consequence local linear subsystems. Then, their gains are designed optimally via a generalized eigenvalue problem (GEVP). Also, the upper-bounds of the matched and unmatched uncertainties are estimated using the adaptive update laws. The multi-objective control aims not only to satisfy the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{2}$ </tex-math></inline-formula> -optimization performance, but also, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula> -stability region is formulated to improve the transient response performance. The <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{2}$ </tex-math></inline-formula> -optimization characterization and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula> -stability design conditions are derived in terms of new linear matrix inequalities (LMIs) conditions. Finally, the effectiveness of the proposed approach is demonstrated by considering a comparative practical example.

Parameter Convergence in Adaptive Control in Presence of Unmatched Uncertainty

The problem of convergence of uncertainties to their true values is of great interest in adaptive control. It is desirable as it facilitates accurate online modeling of structured uncertainties and robust adaptation to disturbances. The adaptation law based on the classical gradient method requires the restrictive persistent excitation (PE) condition to be satisfied for parameter convergence. This paper deals with the relaxation of this PE condition for a class of nonlinear systems in the presence of unmatched uncertainty. The design of the proposed adaptive backstepping controller involves multiple filtered models that translate the restrictive PE condition to linear independence of the filtered regressor models. The proposed controller guarantees asymptotic convergence of the tracking and parameter estimation errors globally in the presence of unmatched uncertainty. Numerical simulations show the efficacy of the proposed controller.

Universal Adaptive Control of Nonlinear Systems

This letter develops a new direct adaptive control framework that extends the certainty equivalence principle to general nonlinear systems with unmatched model uncertainties. The approach adjusts the rate of adaptation online to eliminate the effects of parameter estimation transients on stability. The method can be immediately combined with a previously designed or learned feedback policy if a corresponding model-parameterized Lyapunov function or contraction metric is known. Simulation results of various nonlinear systems with unmatched uncertainties illustrate the approach.

Consensus control for a class of linear multiagent systems using a distributed integral sliding mode strategy

In this paper, a consensus framework is proposed for a class of linear multiagent systems subject to matched and unmatched uncertainties in an undirected topology. A linear coordinate transformation is derived so that the consensus protocol design can be conveniently performed. The distributed consensus protocol is developed by using an integral sliding mode strategy. Consensus is achieved asymptotically and all subsystem states are bounded. By using an integral sliding mode control, the subsystems lie on the sliding surface from the initial time, which avoids any sensitivity to uncertainties during the reaching phase. By use of an appropriate projection matrix, the size of the equivalent control required to maintain sliding is reduced which reduces the conservatism of the design. MATLAB simulations validate the effectiveness and superiority of the proposed method.

Regulation of Electric Vehicle Speed Oscillations Due to Uneven Drive Surfaces Using ISMDTC

An unbalance in the electromagnetic torque and the load torque occurs when Electric Vehicles (EVs) are driven through uneven terrains. This leads to non-periodic and time-varying speed oscillations. As a result, torsional vibrations increase and leads to passenger discomfort and mechanical stress on the EV body. The EV drive control should be designed to mitigate these speed oscillations. In this paper, an Integral Sliding Mode Control Based Direct Torque Control (ISM-DTC) of Induction Motor (IM) is proposed to inherit the intrinsic properties of disturbance rejection, robustness against parametric variations, operational uncertainties, and improve the conventional Proportional-Integral (PI)-based DTC (PIDTC) performance in uncertain EV drive conditions. The proposed control is integrated with PIDTC, which maintains the speed and acts as a nominal control. The non-linear ISM loop cancels out the speed fluctuations by balancing the electromagnetic torque with dynamic load torque demand. The proposed control cancels out the matched uncertainties without amplifying the unmatched uncertainties in system dynamics. An analysis of the uncertainty decomposition and control gain derivation is presented. The proposed ISMDTC is verified through simulations and experiments considering different scenarios of torque, reference speed variations, uncertainties, and the standard New European Driving Cycle (NEDC) and Urban Dynamometer Driving Schedule (US) drive test cycles.

Robust active finite-time control of gas compressor system surge in the presence of unmatched disturbance and uncertainty

Active and robust control of surge instability is a special necessity for optimal and safe operation of centrifugal compressors, and for the purpose, this article presents a new hybrid scheme based on fuzzy and terminal sliding mode methods. The Greitzer model is used to design a novel controller when the disturbance instability in the flow and pressure alike the uncertainity in the compressor characteristic curve and throttle valve are embedded in it. The fuzzy approximator is used to estimate the effects of parametric uncertainty and the nonlinear terms, and the robustness of the proposed method is guaranteed using the terminal sliding mode control method. The Lyapunov criterion is utilized to verify the finite-time stability of the closed-loop system. The performance of the presented method is compared with other methods in the literature through simulations in MATLAB software. The results suggest that our designed controller outperforms the existing ones in terms of surge prevention and robustness against unmatched uncertainties and disturbances.

Robust Passivity-based Sliding Mode Control of a Large Class of Nonlinear Systems Subject to Unmatched Uncertainties: A Robot Manipulator Case Study

The existence of unmatched uncertainties is known as a serious challenge for designing a robust sliding mode control (SMC) law for nonlinear systems. To pass over this obstacle, a novel robust passivity-based sliding mode approach is proposed here for a large class of MIMO nonlinear systems. The design procedure is accomplished in two steps in presence of both matched and unmatched uncertainties. First, an efficient adaptive sliding surface is designed based on the passivity concept. The passivity provides a flexible robust structure for the sliding surface and guarantees the global asymptotic stability of the reduced-order equations of the system as well. Furthermore, simple adaptation laws are obtained to eliminate the effects of uncertainties. Then, the robust controller is formulated using the SMC method. As another important advantage, the proposed approach is relaxed from the upper bound’s constraints of the uncertainties. It is also applied to n-link rigid electrically driven robot manipulator as a widely-used practical nonlinear system. The simulation results show the appropriate tracking performance for the industrial selective compliance assembly robot arm (SCARA) in the presence of noisy external disturbances. Also, an extending case is studied with related research to emphasize the potential of the proposed approach.

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.

Event-triggered active disturbance rejection control for a class of networked systems with unmatched uncertainties: Theoretic and experimental results

In this work, an event-triggered control problem for a class of networked systems with unmatched uncertainties is investigated based on an active disturbance rejection control approach. To estimate the effect of unmatched uncertainties, a bank of extended state observers with guaranteed convergence is proposed. Based on the obtained estimates, a tracking-differentiator-enabled Zeno-free event-triggering condition is introduced with reduced sampling cost. An event-triggered controller is then designed to guarantee the closed-loop stability of the networked system with unmatched uncertainties, leveraging a backstepping control approach. Implementation issues of the proposed approach are discussed, and the effectiveness of the results is illustrated through experimental results on a DC torque motor platform.

Extend Disturbance Observer of Backlash-Based Robust Sliding-Mode Control

The backlash by the hysteresis between the input and the output is always present in the inertial stabilized platform, which will seriously affect the dynamic performance of the platform system at low speed. So, the backlash has been paid more and more attention for the use in the inertial stabilized platform. To handle such a situation, extend disturbance observer (EDOB) has a high advantage to compensate the disturbance caused by backlash. However, some research studies show that the observation effect for some fast time-varying disturbances is satisfactory, which will strict limits on the rate of change in disturbance and still hamper its application; consequently, this paper proposes a sliding-mode-based extend disturbance observer (SMEDO) to compensate backlash. By well-designed sliding-mode surface, it is unnecessary to measure the whole state and the lack of robustness against unmatched uncertainties of the resulting controller, and the robustness and accuracy of modified disturbance observer can be enhanced. Experiments were carried out on a DSP-based platform with backlash in the pitch shafting. The obtained experimental results demonstrate that the SMEDO scheme has an improved performance with the dynamic performance and shafting transmission accuracy compared with the traditional methods.

Reduced-order disturbance observer-based adaptive reaching law control for discretized MIMO systems with unmatched uncertainties

In this paper, an adaptive discrete-time sliding mode control based on reduced-order disturbance observer is proposed for discretized multi-input multi-output systems subjected to unmatching condition. By using the designed discrete reduced-order disturbance observer, a new sliding surface is constructed to counteract the unmatched uncertainties. Then, to guarantee a smaller width of the quasi-sliding mode domain, an adaptive reaching law is developed, whose switching gain is adaptively tuned to prevent overestimation of disturbance on the premise of ensuring the reaching condition of sliding surface; meanwhile, the ranges of the quasi-sliding mode band and attractiveness region are deduced. The proposed control algorithm has low computational complexity and needs no information about the upper bound of unmatched uncertainty. The simulations on the control of a bank-to-turn missile demonstrates that the proposed method can effectively reject unmatched disturbance and provide higher accuracy in comparison with traditional methods.

L₁-Adaptive Robust Control Design for a Pressurized Water-Type Nuclear Power Plant

This work proposes adaptive control-based design strategies to control a pressurized water reactor (PWR) nuclear power plant (NPP). An L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -adaptive-based state-feedback control technique is proposed using the linear quadratic Gaussian control and projection-based adaptation laws. The control scheme possesses good robustness capabilities in handling disturbances and uncertainties. A robust L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -adaptive control technique is also proposed by combining the L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -adaptive control with the loop transfer recovery (LTR) technology. The framework hence gives the strengthened robust set-point tracking performance given the matched and unmatched uncertainties and disturbances. The NPP model employed in this article is defined by five inputs, five outputs, and 38 state variables. A linear model for controller design is obtained by linearizing the nonlinear NPP model at operating conditions. Various simulations are carried out on subsystems of the NPP to verify the effectiveness of the proposed scheme. Numerical and statistical measures are computed for quantitative analysis of the controllers' performance. Several classical control design techniques are also implemented, and their performance is compared with the proposed adaptive control techniques.

A new robust discrete-time sliding mode control design for systems with time-varying delays on state and input and unknown unmatched parameter uncertainties

This paper proposes a new robust Discrete-Time Sliding Mode Control (dt-smc) scheme for linear discrete-time delay system. The delays, affecting the state and the input, are assumed to be known, time-varying and bounded. The considered system is also subject to time-varying Unknown But norm-Bounded (ubb) unmatched uncertainties, that act on the state and the delayed state vectors. The designed controller is based on a novel sliding surface. Using a new Lyapunov functional candidate and by introducing slack variables, a less conservative delay-dependent sufficient condition ensuring the asymptotic stability of the closed loop system is derived in terms of Linear Matrix Inequalities (lmis). With respect to that condition a new dt-smc law is synthesized. The proposed control algorithm is applied to an Autonomous Underwater Vehicle (auv). The simulation results demonstrate the effectiveness of the proposed controller.

Full-Order Terminal Sliding-Mode-Based Sensorless Control of Induction Motor With Gain Adaptation

This article proposes a sensorless speed control approach of Induction motor (IM) applying full-order terminal sliding-mode (FOTSM) control theory. The speed control system consists of three feedback control loops, i.e., the speed-, flux-, and current-loops. The related controllers in these three feedback loops are designed using FOTSM to enhance the robustness and dynamic performance, eliminate the singularity, and attenuate the chattering. The virtual control technique is utilized in the outer-loop speed controller to compensate unmatched uncertainties in the system, such as load disturbance and some parameter variations. The integral-type continuous control law with gain adaptation algorithm guarantees that the current references are smooth. In the inner-loop controllers, the actual voltage control signals can force the tracking errors of the currents to converge to its equilibrium point within finite time. Meanwhile, the FOTSM observer is designed for estimating the flux and speed of the motor simultaneously. Finally, the experiment results have demonstrated the effectiveness and feasibility of the proposed sliding-mode controllers and observers for the sensorless speed control of IM.

Design bounded robust controller using HJB solution for the nonlinear hybrid dynamical systems

This paper deals with the bounded robust controller design for event wise multiple models of the nonlinear hybrid dynamical systems (NHDS) with matched and unmatched uncertainties. The Hamilton-Jacobi-Bellman (HJB) equation based bounded robust control problem is proposed using a suitable non-quadratic term in the objective function of event wise local linearized model. The families of local bounded control laws are designed, to enforce stability using Lyapunov theorem for the individual events with the knowledge of the maximum bound of uncertainty. Using direct method of Lyapunov stability, the local bounded control law is shown to be optimal with respect to the objective function of the system under uncertainty. The new generalized Lyapunov function is proposed with crisp logic variables to establish the stability around the equilibrium points using bounded robust control law. Simulation and experimental results are presented, which validates the proposed bounded robust control approach.

Design of a Fuzzy Adaptive Sliding Mode Control System for MEMS Tunable Capacitors in Voltage Reference Applications

Micro electro mechanical system (MEMS) tunable capacitors (TC) are major elements in ac voltage reference sources (VRS). Physical parametric uncertainties, external electrostatic disturbance, and measurement noise malfunction their operation and ruin the preciseness of the VRS output voltage. Our objective problem is the design of a controller to cope with the mentioned parametric uncertainties, noise, and disturbance. Our applied method is the design and employment of a proportional integral fuzzy adaptive sliding mode controller (FASMC). Both terms of matched and unmatched uncertainties as well as external disturbance and measurement noise are all addressed in this article to generate a stable VRS output for the first time. Not only does this article contribute to the employment of a FASMC to enhance robustness in the drive of the capacitor, but also it benefits the reduction of the chattering effect due to fuzzy regulation in the switching term of the control law. Moreover, the automatic fuzzy adjustment in the controller, which is used for estimation of the coefficients in the sliding surface error dynamical equation, facilitates the specification of those coefficients, which can be time consuming in simulation affairs. Clarifying the importance of the proposed fuzzy adaptive sliding mode controller, this article reviews some previous controllers for MEMS TC in comparison with the proposed fuzzy controller, demonstrating its enhancement in comparison with previous schemes.

An adaptive sliding mode controller design to cope with unmatched uncertainties and disturbance in a MEMS voltage reference source

Tunable micro-electro-mechanical systems (MEMS) capacitors as the fundamental parts are embedded in MEMS AC voltage reference sources (VRS). Being concerned with the accuracy of the output voltage in the reference sources, it gets important to address uncertainties in the physical parameters of the MEMS capacitor. The uncertainties have the great inevitable potentiality of bringing about output voltage perturbation. The output deterioration is more remarkable when the uncertainties are accompanied by disturbance and noise. Manufacturers have been making great attempts to make the MEMS adjustable capacitor with desired rigorous physical characteristics. They have also tried to mitigate physical parameter veracity. However, ambiguity in the values of the parameters inescapably occurs in fabrication procedures since the micro-machining process might itself suffer from uncertainties. Employing a proportional integral (PI) adaptive sliding mode controller (ASMC), both terms of matched and unmatched uncertainties as well as the disturbance, are addressed in this work for the MEMS AC VRS so that a strict voltage is stabilized while the system is simultaneously subjected into uncertainties and exogenous disturbance. Cross-talk, some inertial forces, and electrostatic coercions may appear as matched and unmatched disturbances. Alteration in stiffness and damping coefficients might also take place as matched uncertainties due to variations in the fabrication process or even working environment. The simulation results in the paper are persuasive and the controller design has shown a satisfactory tracking performance.