Single-input And Single-output Research Articles

A Novel Higher-Order Model-Free Adaptive Control for a Class of Discrete-Time SISO Nonlinear Systems

In this work, a novel higher-order model-free adaptive control scheme is presented based on a dynamic linearization approach for a class of discrete-time single input and single output (SISO) nonlinear systems. The control scheme consists of an adaptive control law, a parameter estimation law, and a reset mechanism. The design and analysis of the proposed control approach depends merely on the measured input and output data of the controlled plant. The control performance is improved by using more information of control input and output error measured from previous sampling time instants. Rigorous mathematical analysis is developed to show the bounded input and bounded output (BIBO) stability of the closed-loop system. Two simulation comparisons show the effectiveness of the proposed control scheme.

Adaptive fuzzy control of uncertain stochastic nonlinear systems with unknown dead zone using small-gain approach

This paper considers the adaptive fuzzy robust control problem for a class of single-input and single-output (SISO) stochastic nonlinear systems in strict-feedback form. The systems under study possess unstructured uncertainties, unknown dead-zone, uncertain dynamics and unknown gain functions. In the controller design, fuzzy logic systems are adopted to approximate the unknown functions, and the uncertain nonlinear system is therefore transformed into an uncertain parameterized system with unmodeled dynamics. By combining the backstepping technique with the stochastic small-gain approach, a novel adaptive fuzzy robust control scheme is developed. It is shown that the proposed control approach can guarantee that the closed-loop system is input-state-practically stable (ISpS) in probability, and the output of the system converges to a small neighborhood of the origin by appropriately tuning several design parameters. Simulation results are provided to illustrate the effectiveness of the proposed control approach.

Criterion of the Relative Degree Applied to Design of Multivariable Systems

The question, whether and when the criterion of the relative degree equal to one (RD1), may be applied for designing a multivariable system, is analyzed in the paper. The criterion is commonly utilized in sliding mode control in the case of the plants with single input and single output (SISO). For the multivariable case, first the decoupling of the fast transients is proposed, basing on a conversion of the matrix transfer function (MTF) description of the plant. Then, the controllers with high gain and derivatives are designed separately for each plant output, using the criterion RD1. It is noticed that the same approach may be applied for the multivariable systems with sliding mode control. It is noticed that both the multivariable systems: continuous with control saturation and relay with sliding mode control are in some sense equivalent. The considerations of the paper are confirmed by the performed simulations.

Design and implementation of decoupled compensation for a twin rotor multiple‐input and multiple‐output system

This study achieves compensation of a physical twin rotor multiple-input and multiple-output system in two steps: (i) input–output decoupling its transfer function model, obtained by linearising its non-linear model around an operating point, using an open-loop, minimal precompensator and (ii) effecting 2-degree of freedom single-input and single-output (SISO) compensations for the resulting SISO-decoupled units. While step (i) ensures decoupling in the responses, the other performances (such as robustness, tracking, disturbance rejection, etc.) can be achieved using SISO compensations in step (ii) above. The performances of the compensated system in respect of decoupling, loop robustness and disturbance rejection are verified through simulations and experiments. The results are also compared with the existing ones.

Terminal sliding mode tracking control for a class of SISO uncertain nonlinear systems

In this paper, the terminal sliding mode tracking control is proposed for the uncertain single-input and single-output (SISO) nonlinear system with unknown external disturbance. For the unmeasured disturbance of nonlinear systems, terminal sliding mode disturbance observer is presented. The developed disturbance observer can guarantee the disturbance approximation error to converge to zero in the finite time. Based on the output of designed disturbance observer, the terminal sliding mode tracking control is presented for uncertain SISO nonlinear systems. Subsequently, terminal sliding mode tracking control is developed using disturbance observer technique for the uncertain SISO nonlinear system with control singularity and unknown non-symmetric input saturation. The effects of the control singularity and unknown input saturation are combined with the external disturbance which is approximated using the disturbance observer. Under the proposed terminal sliding mode tracking control techniques, the finite time convergence of all closed-loop signals are guaranteed via Lyapunov analysis. Numerical simulation results are given to illustrate the effectiveness of the proposed terminal sliding mode tracking control.

A FRACTIONAL ORDER UNIVERSAL HIGH GAIN ADAPTIVE STABILIZER

In this paper, a fractional order universal high gain adaptive stabilizer is proposed which guarantees the Lp stability of fractional order multiple–input and multiple–output (MIMO) systems with finite control effort. The boundedness of the control gain for the fractional order universal adaptive strategy is discussed for fractional order MIMO systems, and an upper bound of the control gain is presented for fractional order single-input and single-output (SISO) systems. Some advantages of the discussed fractional order universal adaptive stabilizer are demonstrated in numerical simulations, such as the overshoots of system outputs can be efficiently reduced by decreasing the fractional order of the universal adaptive stabilizer without significantly increasing the system gains.

A New Elementary Operation Approach to Multidimensional Realization and LFR Uncertainty Modeling: The MIMO Case

This paper proposes a new elementary operation approach (EOA) to multidimensional (-D) realization and linear fractional representation (LFR) modeling for multi-input and multi-output (MIMO) -D systems, as an extension of the new EOA proposed for the single-input and single-output (SISO) case by the authors recently. It is shown that, due to the substantial differences between the SISO and MIMO systems, the extension is not straightforward and further significant development is necessary. A matrix relation property among the associated matrices under the augmenting and admissible elementary operations is first revealed. Based on this matrix relation property, the realization problem for the MIMO -D case is formulated as an elementary operation problem of a certain -D polynomial matrix, which makes the extension possible. General constructive procedures are then established for the regular realizations based on the right and left matrix fraction descriptions (MFDs) of a given transfer matrix, respectively, such that one can easily implement this approach by a computer program in, e.g., MATLAB or Maple. Numerical and symbolic examples are provided to illustrate the main ideas and the effectiveness of the proposed approach.

Stability analysis and design of reset control systems with discrete-time triggering conditions

In a reset control system, reset actions are usually triggered whenever a continuous signal crosses a hyperplane. In the computer-based implementation, however, the continuous triggering signal is sampled and the triggering condition is then replaced by a discrete-time counterpart. In this work, we are concerned with the stability analysis and design of reset control systems based directly on discrete-time triggering conditions. First, a relationship between reset control systems and switched systems is established and some stability criteria are then obtained. Second, it is revealed through an example that a well-designed reset control system can be regarded as a hybrid system combining an underdamped baseline system with an overdamped reset mode. The reset matrix, which is assumed to be zero in general, can be adjusted to increase the damping ratio and thus further improve the transient performance. Based on this observation, a design guideline for single-input and single-output (SISO) systems is proposed. Lastly, a hard disk drive example is investigated to demonstrate the proposed design procedure.

Novel Modeling Method for Networked Control Systems with Packet Disordering

This paper focuses on the modeling problem for networked control systems subject to packet disordering. Both network-induced delay and packet loss are taken into consideration. In constructing the model, we first present the novel model for single input and single output (SISO) networked control systems based on the displacement values of packets in terms of switched systems theory, and then which can be extended to the case in multiple input and multiple output (MIMO) networked control systems with packet disordering. The merits or advantages of the modeling method proposed include describing fully the phenomenon of packet disordering, guaranteeing the newest signals to be executed and extensive applicability.

Adaptive sampled-data output tracking of parametric strict-feedback non-linear systems

In this study, the authors address the problem of output tracking for single-input and single-output (SISO) parametric strict-feedback (PSF) non-linear systems in the presence of uncertain parameters under adaptive sampled-data control. The main contributions of this work are twofold: (i) the authors develop a systematic design procedure for adaptive sampled-data controller by combining the backstepping technique with two kinds of discretisation approaches; and (ii) they also provide a theoretical analysis for the performance of sampled-data controller, which shows that the proposed adaptive sampled-data controller can regulate the tracking error to any given neighbourhood of the origin and the state of the sampled-data closed-loop system is bounded. Finally, an illustrative example is given to demonstrate the effectiveness of the presented method.

Non-linear sliding surface: towards high performance robust control

The study proposes a method to design a non-linear sliding surface to achieve better transient response for a class of single-input and single-output (SISO) non-linear uncertain system represented in a Brunowsky canonical form. The proposed surface can also be used for linear uncertain systems with matched perturbations. The proposed surface increases the damping ratio of the closed-loop system from its initial low value; as the output approaches the setpoint from its initial value. Initially, the system is lightly damped resulting in a quick response and as the output approaches the setpoint, the system is overdamped to avoid overshoot. The existence of sliding mode is proved and a new control law is proposed to enforce sliding motion. The scheme is able to achieve low overshoot and short settling time simultaneously which is not possible with a linear sliding surface. To ease the synthesis of the non-linear surface, linear matrix inequalities-based algorithm is proposed. Effectiveness of the proposed scheme is illustrated by the simulation results.

Layered Video Transmission with Network Coding in a Cooperative Virtual MIMO Cellular Relay Networks

In this letter, we propose a layered video streaming technique that combines network coding (NC), multiple-input multiple-output (MIMO), and hierarchical modulation (HM) over cellular relay networks. We provide a performance analysis of different transmission modes of NC and MIMO in terms of the error rate in video layers, which is reflected in the total layered-video quality. The HM is used to differentiate the error rates among video layers. The simulation results show that the NC, the MIMO spatial multiplexing (SM), and the combination of both the NC and MIMO-SM gives video-quality gains of about 1.9dB, 6dB, and 12dB maximally, respectively, compared to the conventional single-input and single-output (SISO) single relay network (SRN) system.

Dynamic Model Identification of the Main Steam Temperature for Supercritical Once-through Boiler

In this paper the dynamic model of single-input and single-output (SISO) is established, which take the coal feed as the input and the main steam temperature as the output. Recursive extended least squares (RELS) was used to identify the system model, and the ideal identification results were achieved. The results showed that the output of identification and actual output in good agreement by usage of the recorded data to verify the accuracy of model further.

Tuning of multi-loop PI controllers based on gain and phase margin specifications

In this paper, a single-iteration strategy is proposed for the design of a multi-loop PI controller to achieve the desired gain and phase margins for two-input and two-output (TITO) processes. To handle loop interactions, a TITO system is converted into two equivalent single loops with uncertainties drawn from interactions. The maximum uncertainty is estimated for the initial controller design in one loop and single-input and single-output (SISO) controller design is applied. This controller is substituted to other equivalent loop for design, and finally, the first loop controller is refined on knowledge of other loop controller. For SISO controller tuning, a new method is presented to determine the achievable gain and phase margins as well as the relevant controller parameters. Examples are given for illustration and comparison.

Unified approach for minimal output dead time compensation in MIMO processes

Abstract This paper presents the development of a unified dead-time compensator for multiple-input and multiple-output (MIMO) n × n processes with multiple delays. The proposed structure is a generalization of the single-input and single-output (SISO) filtered Smith predictor (FSP) controller, therefore, as in the SISO case it can be used to control stable, integrating, and unstable dead-time processes. MIMO-FSP compensates the minimal output dead time and its tuning is simple and can be performed considering a trade-off between performance and robustness. Several simulation case studies are used in the paper to illustrate the use of the unified approach and also to compare the obtained solutions with some recent published results. Practical experiments using a neonatal intensive care unit prototype are also presented.

A Wiener Neural Network-Based Identification and Adaptive Generalized Predictive Control for Nonlinear SISO Systems

In this study, a Wiener-type neural network (WNN) is derived for identification and control of single-input and single-output (SISO) nonlinear systems. The nonlinear system is identified by the WNN, which consists of a linear dynamic block in cascade with a nonlinear static gain. The Lipschitz criteria for model order determination and back propagation for the adjustment of weights in the network are presented. Using the parameters of the Wiener model, the analytical expressions used in the controller, generalized predictive control (GPC) is modified every time step, to handle the nonlinear dynamics of the controlled variable. Finally, the proposed WNN-based GPC algorithm is tested in simulation on several nonlinear plants with different degrees of nonlinearity. Simulation results show that WNN identification approach has better accuracy, in comparison to other neural network identifiers. The WNN-based GPC has better control performance, in comparison to standard GPC.

Center-of-gravity fuzzy systems based on normal fuzzy implications

In this paper, the construction and approximation problem of a single input and single output (SISO) fuzzy system with normal implication and center-of-gravity defuzzifier is discussed. First, the method of a non-singleton fuzzifier for the input variable and the concept of an adaptive universe for the output fuzzy set are proposed. Then, by using this method and this concept of an adaptive universe, SISO fuzzy systems based on center-of-gravity defuzzifier and normal implications such as the Kleene–Dienes implication or the Lukasiewicz implication are constructed. The constructed fuzzy systems have the general form S ¯ ( x ) = A i ∗ ( x ) f ( x i ) + A i + 1 ∗ ( x ) f ( x i + 1 ) , with A i ∗ ( x ) + A i + 1 ∗ ( x ) = 1 , and, furthermore, they are universal approximators. The sufficient conditions for the proposed fuzzy systems to be universal approximators are also obtained. To illustrate the universal property, an example is also given.

Adaptive fuzzy backstepping output feedback control of nonlinear time-delay systems with unknown high-frequency gain sign

In this paper, an adaptive fuzzy robust feedback control approach is proposed for a class of single-input and single-output (SISO) strict-feedback nonlinear systems with unknown nonlinear functions, time delays, unknown high-frequency gain sign, and without the measurements of the states. In the backstepping recursive design, fuzzy logic systems are employed to approximate the unknown smooth nonlinear functions, K-filters is designed to estimate the unmeasured states, and Nussbaum gain functions are introduced to solve the problem of unknown sign of high-frequency gain. By combining adaptive fuzzy control theory and adaptive backstepping design, a stable adaptive fuzzy output feedback control scheme is developed. It has been proven that the proposed adaptive fuzzy robust control approach can guarantee that all the signals of the closed-loop system are uniformly ultimately bounded and the tracking error can converge to a small neighborhood of the origin by appropriately choosing design parameters. Simulation results have shown the effectiveness of the proposed method.

Adaptive stabilisation for a class of non-linear state time-varying delay systems with unknown time-delay bound

In this study, the authors address the problem of adaptive backstepping control for a class of single-input and single-output (SISO) non-linear time-delay systems in triangular structure. Both the parameters of the system to be controlled and the upper bounds of the time delays and their derivatives are assumed to be unknown. A direct adaptive controller for this class of uncertain non-linear systems is proposed. The assumption on delay-related non-linearities is further relaxed. An appropriate Lyapunov–Krasovskii functional is constructed, and the backstepping technique is used. It is shown that all the closed-loop signals are bounded, while the plant states converge to zero asymptotically. A simulation example is provided to demonstrate the design procedure and performance of the proposed method.

Minimal Euclidean distance‐inspired optimal and suboptimal modulation schemes for vector OFDM system

AbstractIn single‐input and single‐output (SISO) systems, the vector orthogonal frequency division multiplexing (VOFDM) has been proposed to reduce the cyclic prefix length, whereas the precoded OFDM has been proposed to overcome spectral‐null channels. However, VOFDM does not show robustness to spectral‐null channels, and the precoded OFDM system has expanded data rate. This work proposes the optimal and suboptimal modulation schemes in vector OFDM systems with knowledge of the channel impulse response (CIR) in order to reduce the bit error rate (BER). As the BER performance is determined by the diversity of the received vector symbols, the proposed modulation scheme mainly concerns the minimal Euclidean distance of all the possible received vector symbols. Through the analysis of the vector input and output equations, we derive the Euclidean distance of the received vector symbols. Then, we propose optimal and suboptimal modulation schemes in VOFDM system to overcome spectral‐null channels by improving the minimal Euclidean distance. Both theoretical performance analysis and simulation results are presented to show the robustness of our system. Finally, we conduct a compared performance analysis of the proposed VOFDM system, the conventional precoded OFDM system, and the conventional VOFDM system. Copyright © 2010 John Wiley & Sons, Ltd.