Multi-input Multi-output Discrete-time Systems Research Articles

Data-driven fault-tolerant control with fuzzy-rules equivalent model for a class of unknown discrete-time MIMO systems and complex coupling

The problem of fault-tolerant control for a class of discrete-time multi-input–multi-output systems is addressed with actuator faults and complex-coupling property of controlled plants. To avoid the non-causality problem, the equivalent model is established by the proposed coupling-matrix with the fractional input–output data and Multi-input fuzzy rules emulated networks (MiFREN) while the diagonally dominant condition is completely omitted and actuator faults are imitated by the coupling-matrix. Then, another MiFREN is utilized as the direct adaptive controller and the learning law is established to ensure closed-loop performance through rigorous mathematical analysis. The effectiveness of the proposed controller is validated by the numerical system and the activated sludge treatment processes (ASTP) over the comparison results in dealing with complex-coupling, unknown actuator faults, noisy measurements and undefined disturbances.

A note on invertibility and relative degree of MIMO LTI systems

The property of system invertibility is important both from a theoretical standpoint and an important consideration in left and right inversion problems that deal with input estimation and tracking control respectively. Nuances associated with the notion of relative degree in multi-input, multi-output (MIMO) systems on account of input–output delays pose challenges in system inversion problems and are more acute in the case of non-square systems. In this note, using the LTI discrete-time MIMO systems framework, we review existing notions of relative degree and develop new definitions and generalizations for relative degree to help address some of the gaps in system inversion problems. In doing so, we also show through simple but elegant results that existence of well-defined relative degree for an LTI MIMO system implies its invertibility. Furthermore, we also highlight the utility of these ideas in practical tracking control and input estimation situations and problems.

Alternative Generalized Predictive Control for Output Disturbed Multi-Input Multi-Output Discrete-Time Systems

This article proposes an option to execute conveniently the traditional Model Predictive Control (GPC), called the Alternative Generalized Predictive Control (AGPC). In this AGPC the disturbed discrete-time input-output mapping of controlled plant is utilized directly for the prediction of plant outputs, instead of its transfer function as being done in the conventional approach. Hence, solving Diophantine equations will be avoided. Within this AGPC all recorded values of plant inputs/outputs in the last time-horizon are matched into separate vectors for computing predictive control signals at the next control step, which helps therefore that its implementation becomes more manageable. To verify via virtually real simulation the control performance of this proposed AGPC a Simscape water tank model, which is chosen as the controlled plant, had been created among Thermal Fluids Toolbox. The simulation is carried out for two different circumstances, one by using AGPC and the other by applying conventional PID, for comparison purposes. The simulation demonstrates also how to realize this AGPC in practice.

Data-driven discrete terminal sliding mode decoupling control method with prescribed performance

This paper proposes a data-driven terminal sliding mode decoupling controller with prescribed performance for a class of discrete-time multi-input multi-output systems in the presence of external disturbances and uncertainties. First, utilizing a discrete-time extended state observer and a compact form dynamic linearization data model, we derive a new data-driven mothod and establish the relationship between the input and output signals of controlled plant. Moreover, the disturbances, uncertainties, and couplings are suppressed owing to the application of the terminal sliding mode technique. Combined with the principle of prescribed performance control, the terminal sliding mode law with prescribed performance is derived. With the proposed data-driven method, the tracking error is lower, and the decoupling ability is improved. Furthermore, the stability of the control system is proven. Finally, a simulation is conducted on a three-tank system to demonstrate the effectiveness of the proposed scheme.

Data-Driven Iterative Learning Control for Nonlinear Discrete-Time MIMO Systems.

This article considers the tracking control of unknown nonlinear nonaffine repetitive discrete-time multi-input multi-output systems. Two data-driven iterative learning control (ILC) schemes are designed based on two equivalent dynamic linearization data models of an unknown ideal learning controller, which exists theoretically in the iteration domain. The two control schemes provide ways of selecting learning controllers based on the complexity of the controlled nonlinear systems. The learning control gain matrixes of the two learning controllers are optimized through the steepest descent method using only the measured input-output data of the nonlinear systems. The proposed ILC approaches are pure data-driven since no model information of the controlled systems is involved. The stability and convergence of the proposed ILC approaches are rigorously analyzed under reasonable conditions. Numerical simulation and an experiment based on a Gantry-type linear motor drive system are conducted to verify the effectiveness of the proposed data-driven ILC approaches.

Data-Based Adaptive Fault Estimation and Fault-Tolerant Control for MIMO Model-Free Systems Using Generalized Fuzzy Hyperbolic Model

This paper is focused on the data-driven model-free adaptive fault detection and estimation (FDE) and fault-tolerant control (FTC) problems for multi-input multi-output (MIMO) discrete-time systems with unknown sensor faults. First, in the light of the compact form dynamic linearization method, the initial systems are transformed into a novel data-based model with only one unknown parameter. Second, a fault estimator is established to detect the sensor faults. Noting that a time-varying residual threshold is developed to determine whether the sensor faults occur or not. Then, the unknown faults are approximated based on the powerful approximation capability of a generalized fuzzy hyperbolic model and the FTC approaches are reconstructed by applying the optimality criterion. In contrast to the previous schemes, the main contributions are twofold: first, it is the first time to solve the FDE and FTC problems for model-free MIMO discrete-time systems; second, the proposed FTC policy is simple to be implemented with reducing computational burden. Finally, two examples are used to demonstrate the effectiveness of the proposed FDE and FTC methods.

Adaptive Critic Design for Pure-Feedback Discrete-Time MIMO Systems Preceded by Unknown Backlashlike Hysteresis

This paper concentrates on the adaptive critic design (ACD) issue for a class of uncertain multi-input multioutput (MIMO) nonlinear discrete-time systems preceded by unknown backlashlike hysteresis. The considered systems are in a block-triangular pure-feedback form, in which there exist nonaffine functions and couplings between states and inputs. This makes that the ACD-based optimal control becomes very difficult and complicated. To this end, the mean value theorem is employed to transform the original systems into input-output models. Based on the reinforcement learning algorithm, the optimal control strategy is established with an actor-critic structure. Not only the stability of the systems is ensured but also the performance index is minimized. In contrast to the previous results, the main contributions are: 1) it is the first time to build an ACD framework for such MIMO systems with unknown hysteresis and 2) an adaptive auxiliary signal is developed to compensate the influence of hysteresis. In the end, a numerical study is provided to demonstrate the effectiveness of the present method.

Adaptive control for MIMO nonlinear systems based on PID neural networks

In this paper a real time control technique for a nonlinear discrete time Multi-input Multi-output systems is presented. The proposed technique is based on the combination of PID controller properties and neural networks characteristic of self-learning and flexibility of function presentation. The standard back propagation (BP) algorithm is used to find parameters of the PID neural network controller. The suggested technique modifies the architecture used in SISO to fit with MIMO systems. The experimental results are presented toward the end of the paper to show the effectiveness of the proposed technique

Robust sliding mode learning control for uncertain discrete‐time multi‐input multi‐output systems

A robust sliding mode-based learning control scheme is newly developed for a class of uncertain discrete-time multi-input multi-output systems. In particular, a recursive-learning controller is designed to enforce the sliding variable vector to reach and remain on the intersection of the sliding surfaces, and the system dynamics is then guaranteed to asymptotically converge to zero on the pre-described sliding manifold with respect to uncertainty. The `Lipschitz-like condition' for sliding mode control systems, which presents an essential property of the continuity of uncertain systems, is further extended to the discrete-time case establishing in this study. The appealing attributes of this approach include: (i) the knowledge of the bounds of the uncertainties is not required for the controller design, (ii) the closed-loop system exhibits a strong robustness against uncertain dynamics and (iii) the control scheme enjoys the chattering-free characteristic. Simulation results are given to illustrate the effectiveness of the proposed control technique.

Adaptive fuzzy sliding mode control for uncertain multi-input multi-output discrete-time systems using a set of noisy measurements

This paper is concerned with the design of an adaptive fuzzy sliding mode control (AFSMC) for uncertain nonlinear multi-input multi-output (MIMO) dynamic systems using a set of noisy measurements. The dynamic systems to be considered here are described by a discrete-time nonlinear state equation with mismatched uncertainties, and the states are measured by the restriction of measurement sensors and the contamination of independent random noises. The estimates for the unmeasurable states and the uncertainties are obtained by using the weighted extended Kalman filter. In the design of the proposed AFSMC, the adaptive switching factor characterising the switching control is designed using the fuzzy inference approach where the unknown gain of the switching control is assumed to be a positive definite matrix. It is proved that under some conditions the estimation errors will converge to zero as the time tends to infinity, and the states are ultimately bounded under the action of the proposed AFSMC. The effectiveness of the proposed method is indicated through the simulation experiment of an active suspension system for a half-car model.

Robust adaptive NN control for a class of uncertain discrete-time nonlinear MIMO systems

A robust adaptive NN output feedback control is proposed to control a class of uncertain discrete-time nonlinear multi-input–multi-output (MIMO) systems. The high-order neural networks are utilized to approximate the unknown nonlinear functions in the systems. Compared with the previous research for discrete-time MIMO systems, robustness of the proposed adaptive algorithm is obvious improved. Using Lyapunov stability theorem, the results show all the signals in the closed-loop system are semi-globally uniformly ultimately bounded, and the tracking errors converge to a small neighborhood of zero by choosing the design parameters appropriately.

Adaptive sliding mode control for discrete-time multi-input multi-output systems

In this paper, robust adaptive sliding mode tracking control for discrete-time multi-input multi-output systems with unknown parameters and disturbance is considered. The robust tracking controller is comprised of adaptive control and sliding mode control design. Bounded motion of the system around the sliding surface and stability of the global system in the sense that all signals remain bounded are guaranteed. If the disturbance and the reference signal are slowly varying with respect to the sampling frequency, the proposed sliding mode controller can reject the disturbance and output tracking can be approximately achieved. Simulation results are presented to illustrate the proposed approach.

Identification of discrete-time MIMO systems using a class of observable canonical-form

The paper presents an identification algorithm for a discrete-time (D-T) multiinput multioutput (MIMO) deterministic system. The proposed identification algorithm which is based on calculating a matrix fraction description (MFD) from available input-output data can be considered as a version of the recently developed subspace model identification (SMI) schemes. The system to be identified is represented using a special class of observable canonical-forms which have the property that all its observability indices are equal. The used observable canonical-form is convenient in the sense that it makes the identification problem of the MIMO systems very similar to that of the single-input single-output (SISO) systems. The theoretical developments are verified through the use of the proposed algorithm to identify a minimal order state space model of a boiler used in the petroleum industry in Kuwait.

An approach for improved modal control of multi-input multi-output discrete time systems†

Abstract It is shown that the state feedback gains for a given multi-input multi-output discrete time system can be computed by matching a finite model output sequence members to prespecified ones. Relationship of the pole positioning control schemes to such matching is first examined and it is shown that better control is possible by adopting the method proposed in this paper. The results are illustrated through a numerical example.