Observer-based Controller Design Research Articles

Observer-based output feedback control of networked control systems with non-uniform sampling and time-varying delay

ABSTRACTThis paper investigates the problem of observer-based output feedback control for networked control systems with non-uniform sampling and time-varying transmission delay. The sampling intervals are assumed to vary within a given interval. The transmission delay belongs to a known interval. A discrete-time model is first established, which contains time-varying delay and norm-bounded uncertainties coming from non-uniform sampling intervals. It is then converted to an interconnection of two subsystems in which the forward channel is delay-free. The scaled small gain theorem is used to derive the stability condition for the closed-loop system. Moreover, the observer-based output feedback controller design method is proposed by utilising a modified cone complementary linearisation algorithm. Finally, numerical examples illustrate the validity and superiority of the proposed method.

Observer-Based Output-Feedback Control Design for a Class of Nonlinear Switched T–S Fuzzy Systems with Actuator Saturation and Time Delay

A state observer-based output-feedback controller is proposed for a class of nonlinear switched T–S fuzzy systems with actuator saturation and time delay in this paper. The proposed control scheme is developed by applying the parallel distributed compensation technique. The nonlinear switched fuzzy systems consist of several switched modes, and each switched mode is linear system. Therefore, by using Lyapunov function theory and average dwell time approach, the sufficient stability conditions are given. The effectiveness and feasibility of the proposed scheme are verified through numerical and practical examples.

Output feedback stabilization of switching discrete-time linear systems with parameter uncertainties

This paper deals with observer-based control design for a class of switched discrete-time linear systems with parameter uncertainties. The main contribution of the paper is to propose a convenient way based on Finsler’s lemma to enhance the synthesis conditions, expressed in terms of Linear Matrix Inequalities (LMIs). Indeed, this judicious use of Finsler’s lemma provides additional decision variables, which render the LMIs less conservative and more general than all those existing in the literature for the same class of systems. Two numerical examples followed by a Monte Carlo evaluation are proposed to show the superiority of the proposed design technique.

Observer-based iterative learning control design in the repetitive process setting

This paper considers the design of an observer-based iterative learning control law for discrete linear systems using repetitive process stability theory The resulting design produces a stabilizing feedback controller in the time domain and a PD-type of feedforward controller that guarantees monotonic convergence in the trial-to-trial domain. Furthermore, the new design procedure includes limited frequency range specifications, which will be of particular interest in some applications. All design computations required for the new results in this paper can be completed using linear matrix inequalities. A simulation example is given to illustrate the theoretical developments.

Observer-Based Boundary Control Design for the Suppression of Stick–Slip Oscillations in Drilling Systems With Only Surface Measurements

We develop an observer-based boundary controller for the rotary table to suppress stick–slip oscillations and to maintain the angular velocity of the drill string at a desired value during a drilling process despite unknown friction torque and by using only surface measurements. The control design is based on a distributed model of the drill string. The obtained infinite dimensional model is converted to an ordinary differential equation–partial differential equation (ODE–PDE) coupled system. The observer-based controller is designed by reformulating the problem as the stabilization of an linear time-invariant (LTI) system which is affected by a constant unknown disturbance and has simultaneous actuator and sensor delays. The main contribution of the controller is that it requires only surface measurements. We prove that the equilibrium of the closed-loop system is exponentially stable, and that the angular velocity regulation is achieved with the estimations of unknown friction torque and drill bit velocity. The effectiveness of the controller is demonstrated using numerical simulations.

Command-Filtered-Based Fuzzy Adaptive Control Design for MIMO-Switched Nonstrict-Feedback Nonlinear Systems

The adaptive fuzzy tracking control design problem for multi-input and multi-output uncertain switched nonstrict-feedback nonlinear systems with arbitrary switchings is investigated in this paper. Fuzzy logic systems are introduced to identify the unknown nonlinear functions (for state measurable case) and model the uncertain nonlinear systems (for state immeasurable case). Both state feedback and observer-based output feedback control design schemes are developed based on combined command filter and adaptive fuzzy control technique. The proposed adaptive fuzzy controllers not only solve the “explosion of complexity” problem existing in conventional backstepping control schemes, but as well as avoid the calculation of partial derivatives. Furthermore, the stability of the fuzzy control systems under arbitrary switchings is proven based on the common Lyapunov function method. Two simulation examples are presented to further demonstrate the effectiveness of the proposed control strategies.

Observer-based control for a singular Markovian jumping system

PurposeFor most practical control system problems, the state variables of a system are not often available or measureable due to technical or economical constraints. In these cases, an observer-based controller design problem, which is involved with using the available information on inputs and outputs to reconstruct the unmeasured states, is desirable, and it has been wide investigated in many practical applications. However, the investigation on a discrete-time singular Markovian jumping system is few so far. This paper aims to consider an observer-based control problem for a discrete-time singular Markovian jumping system and provides a set of easy-used conditions to the proposed control law.Design/methodology/approachAccording to the connotation of the separation principle extended from linear systems, a mode-dependent observer and a state-feedback controller is designed and carried out independently via two sets of derived necessary and sufficient conditions in terms of linear matrix inequalities (LMIs).FindingsA set of necessary and sufficient conditions for an admissibility analysis problem related to a discrete-time singular Markovian jumping system is derived to be a doctrinal foundation for the proposed design problems. A mode-dependent observer and a controller for such systems could be designed via two sets of strictly LMI-based synthesis conditions.Research limitations/implicationsThe proposed method can be applied to discrete-time singular Markovian jumping systems with transition probability pij > 0 rather than the ones with pii = 0.Practical implicationsThe formulated problem and proposed methods have extensive applications in various fields such as power systems, electrical circuits, robot systems, chemical systems, networked control systems and interconnected large-scale systems. Take robotic networked control systems for example. It is recognized that the variance phenomena derived from network transmission, such as packets dropout, loss and disorder, are suitable for modeling as a system with Markovian jumping modes, while the dynamics of the robot systems can be described by singular systems. In addition, the packets dropout or loss might result in unreliable transmission signals which motivates an observer-based control problem.Originality/valueBoth of the resultant conditions of analysis and synthesis problems for a discrete-time singular Markovian jumping system are necessary and sufficient, and are formed in strict LMIs, which can be used and implemented easily via MATLAB toolbox.

Reliable Output Feedback Control for T-S Fuzzy Systems With Decentralized Event Triggering Communication and Actuator Failures.

Due to the unavailability of full state variables in many control systems, this paper is concerned with the design of reliable observer-based output feedback controller for a class of network-based Takagi-Sugeno fuzzy systems with actuator failures. In order to better allocate network resources under the case that the sensor nodes are physically distributed, the decentralized event triggering communication scheme is adopted such that each sensor node is capable to determine the transmission of its local measurement information independently. Considering that the implementation of the controller may not be synchronized with the plant trajectories due to asynchronous premise variables with such communication mechanism, a novel piecewise fuzzy observer-based output feedback controller is developed. By applying a piecewise Lyapunov function and some techniques on matrix convexification, an approach to the design of observer and controller gain is derived for the augmented closed-loop system to be asymptotically stable with a guaranteed H∞ performance and reduced transmission frequency. Finally, two examples are given to show the effectiveness of the developed method.

$H_\infty$ dynamical observer-based control for descriptor systems

This paper addresses the problem of $H_\infty$ observer-based control design for descriptor systems. A new concept of dynamical observer-based control is introduced for linear descriptor systems. The main advantage of this concept is the structure of this dynamical observer, which is more general than those founded in the literature. By using this general structure, particular cases such as the proportional and the proportional-integral observers (PIOs) can be directly deduced. Necessary and sufficient conditions under which the controlled output converges asymptotically to zero are given in a set of linear matrix inequalities formulation. Numerical examples comparing our approach with the proportional and the PIO (deduced from the dynamical observer), and with a functional filter-based controller previously reported in the literature, are respectively presented.

Observer-Based Controller Design for a Class of Nonlinear Networked Control Systems with Random Time-Delays Modeled by Markov Chains

This paper investigates the observer-based controller design problem for a class of nonlinear networked control systems with random time-delays. The nonlinearity is assumed to satisfy a global Lipschitz condition and two dependent Markov chains are employed to describe the time-delay from sensor to controller (S-C delay) and the time-delay from controller to actuator (C-A delay), respectively. The transition probabilities of S-C delay and C-A delay are both assumed to be partly inaccessible. Sufficient conditions on the stochastic stability for the closed-loop systems are obtained by constructing proper Lyapunov functional. The methods of calculating the controller and the observer gain matrix are also given. Two numerical examples are used to illustrate the effectiveness of the proposed method.

Observer-Based Robust Controller Design for Nonlinear Fractional-Order Uncertain Systems via LMI

We discuss the observer-based robust controller design problem for a class of nonlinear fractional-order uncertain systems with admissible time-variant uncertainty in the case of the fractional-order satisfying 0<α<1. Based on direct Lyapunov approach, a sufficient condition for the robust asymptotic stability of the observer-based nonlinear fractional-order uncertain systems is presented. Employing Finsler’s Lemma, the systematic robust stabilization design algorithm is then proposed in terms of linear matrix inequalities (LMIs). The efficiency and advantage of the proposed algorithm are finally illustrated by two numerical simulations.

Observer-based controller design for a class of Takagi-Sugeno descriptor systems

Observer-based controller design for a class of Takagi-Sugeno descriptor systems

Generalized predictive control for a coupled four tank MIMO system using a continuous-discrete time observer

This paper deals with the problem of the observer based control design for a coupled four-tank liquid level system. For this MIMO system's dynamics, motivated by a desire to provide precise and sensorless liquid level control, a nonlinear predictive controller based on a continuous-discrete observer is presented. First, an analytical solution from the model predictive control (MPC) technique is developed for a particular class of nonlinear MIMO systems and its corresponding exponential stability is proven. Then, a high gain observer that runs in continuous-time with an output error correction time that is updated in a mixed continuous-discrete fashion is designed in order to estimate the liquid levels in the two upper tanks. The effectiveness of the designed control schemes are validated by two tests; The first one is maintaining a constant level in the first bottom tank while making the level in the second bottom tank to follow a sinusoidal reference signal. The second test is more difficult and it is made using two trapezoidal reference signals in order to see the decoupling performance of the system’s outputs. Simulation and experimental results validate the objective of the paper.

Observer-Based Adaptive Fuzzy Control for Switched Stochastic Nonlinear Systems With Partial Tracking Errors Constrained

This paper discusses the adaptive fuzzy partial tracking errors constrained control problem for a class of uncertain stochastic nonlinear systems. The concerned systems contain the unknown nonlinear functions, unmeasured state variables, and the switching signal with average dwell time. The fuzzy logic systems are first used to approximate the unknown nonlinear functions, and a switched fuzzy state observer is developed for estimating the unmeasured states. By introducing the performance function and error transformation into the backstepping dynamic surface control design, a new observer-based adaptive fuzzy control design approach is developed. By employing the multiple Lyapunov function and the average dwell time methods, it is proved that all the signals of the resulting closed-loop system are bounded, and the partial tracking errors are confined all times within the prescribed bounds. A simulation example is provided to show the effectiveness of the proposed approach.

Adaptive Fuzzy Tracking Control Design for SISO Uncertain Nonstrict Feedback Nonlinear Systems

This paper investigates an adaptive fuzzy tracking control design problem for single-input and single-output uncertain nonstrict feedback nonlinear systems. For the cases of the states measurable and the states immeasurable, fuzzy logic systems are separately adopted to approximate the unknown nonlinear functions or model the uncertain nonlinear systems. In the unified framework of adaptive backstepping control design, both adaptive fuzzy state feedback and observer-based output feedback control design schemes are proposed. The stability of the closed-loop systems is proved by using Lyapunov function theory. The simulation examples are provided to confirm the effectiveness of the proposed control methods.

New observer-based control design for mismatched uncertain systems with time-delay

Abstract In this paper, the state estimation problem for a class of mismatched uncertain time-delay systems is addressed. The estimation uses observer-based control techniques. The mismatched uncertain time-delay systems investigated in this study include mismatched parameter uncertainties in the state matrix and in the delayed state matrix. First, based on a new lemma with appropriately choosing Lyapunov functional, new results for stabilization of mismatched uncertain time-delay systems are provided on the basis of a linear matrix inequality (LMI) framework and the asymptotic convergence properties for the estimation error is ensured. Second, the control and observer gains are given from single LMI feasible solution which can overcome the drawback of the bilinear matrix inequalities approach often reported in the literature. Finally, a numerical example is used to demonstrate the efficacy of the proposed method.

Two time-scale observer-based robust motion controller design and realization of a linear actuator

In this paper, an observer-based sliding mode controller is proposed for a high-accuracy motion plant to suppress the disturbances and improve the tracking performance. In particular, a two time-scale separation technology, which can recover the disturbance state in a faster time scale, is utilized to compensate the disturbances and improve the system robustness. The parameter identification is carried out to obtain the model coefficients with a high fitting rate. Such an identified model can allow the engineers to tune the controller’s gains highly enough when the system suffers from the measurement noises. Instead of the traditional low-pass filter, a differentiator is introduced for the velocity signal prediction and its discrete-time version is provided to attenuate the noises effect. To verify the effectiveness of the proposed approach, an adaptive robust control law is compared with the proposed one in terms of dynamic positioning error, robustness and rapid signal tracking, and the superiority and advantages can be illustrated by the experimental results.

Observer-Based Fuzzy Control for Nonlinear Networked Systems Under Unmeasurable Premise Variables

The problem of fuzzy observer-based controller design is investigated for nonlinear networked control systems subject to imperfect communication links and parameter uncertainties. The nonlinear networked control systems with parameter uncertainties are modeled through an interval type-2 (IT2) Takagi-Sugeno (T-S) model, in which the uncertainties are handled via lower and upper membership functions. The measurement loss occurs randomly, both in the sensor-to-observer and the controller-to-actuator communication links. Specially, a novel data compensation strategy is adopted in the controller-to-actuator channel. The observer is designed under the unmeasurable premise variables case, and then, the controller is designed with the estimated states. Moreover, the conditions for the existence of the controller can ensure that the resulting closed-loop system is stochastically stable with the predefined disturbance attenuation performance. Two examples are provided to illustrate the effectiveness of the proposed method.

Tracking Control of Robotic Manipulators With Uncertain Kinematics and Dynamics

This paper investigates a difficult problem of tracking control for robotic manipulations with guaranteed high accuracy. Uncertain kinematics, unknown torques including unknown gravitational torque, unknown friction torque, and uncertain dynamics induced by uncertain moment of inertia and disturbance, are addressed. The approach is developed in the framework of observer-based control design. Two sliding-mode observers are proposed to handle uncertain kinematics and to estimate unknown torques, respectively. Using the estimated information, a control law is then synthesized to guarantee that the desired trajectory can be followed after finite-time with zero tracking error. Experimental results are presented to show the performance of the proposed control approach.

Observer-based robust control of one-sided Lipschitz nonlinear systems

This paper presents an observer-based controller design for the class of nonlinear systems with time-varying parametric uncertainties and norm-bounded disturbances. The design methodology, for the less conservative one-sided Lipschitz nonlinear systems, involves astute utilization of Young’s inequality and several matrix decompositions. A sufficient condition for simultaneous extraction of observer and controller gains is stipulated by a numerically tractable set of convex optimization conditions. The constraints are handled by a nonlinear iterative cone-complementary linearization method in obtaining gain matrices. Further, an observer-based control technique for one-sided Lipschitz nonlinear systems, robust against L2-norm-bounded perturbations, is contrived. The proposed methodology ensures robustness against parametric uncertainties and external perturbations. Simulation examples demonstrating the effectiveness of the proposed methodologies are presented.