Class Of MIMO Nonlinear Systems Research Articles

Robust tracking control for nonlinear MIMO systems via fuzzy approaches

This paper addresses the problem of designing robust output tracking controls for a class of nonlinear MIMO systems that are represented by input–output models involving plant uncertainties and external disturbances. Hybrid adaptive-robust tracking control schemes which are based upon a combination of the H ∞ tracking theory, VSS control algorithm, and fuzzy control design are developed such that all the states and signals are bounded and an H ∞ tracking control is guaranteed. Consequently, the tracking performance of adaptive fuzzy-based control is greatly improved with the help of robust VSS and H ∞ control algorithms. The H ∞ tracking control design can be extended to treat general uncertain nonlinear systems with the help of adaptive fuzzy approximators.

Robust self-learning fuzzy controller design for a class of nonlinear MIMO systems

A new learning paradigm that can be applied for the design of a fuzzy logic-based learning controller that is robust to external signals such as disturbances and set-point changes is proposed in the paper. It is well known that the self-organizing fuzzy controller proposed by Procyk and Mamdani is sensitive to external signals. Such a phenomenon may be observed in other types of direct fuzzy logic-based learning controllers that utilize an adaptation scheme in which the locational information of the current error state vector determines the degree of adaptation that should be made in the learning controller. To resolve the problem of sensitivity to external signals, it is proposed that learning and modification of the controller be made in consideration of the motional trend of the error state vector as well as its locational information. This paradigm is adopted in the design of a new robust self-learning fuzzy controller for a class of nonlinear MIMO systems. The well-known techniques of sliding mode control and the fuzzy decision making method are utilized to implement the proposed learning scheme in the fuzzy learning controller. Via simulation study and experimental results, the proposed learning controller is verified to be robust in the presence of external disturbances.

Nonminimum phase tracking in MIMO systems with square input–output dynamics via dynamic sliding manifolds

The approximate causal output tracking problem in nonlinear multi-input/multi-output (MIMO) nonminimum phase systems is addressed via sliding mode control. A class of MIMO nonlinear systems with matched nonlinearities as well as matched and unmatched disturbances, where the number of inputs, outputs, and the total relative degree are equal, is considered. The output tracking problem is solved using dynamic sliding manifold technique. The linear bounded error dynamics with desired eigenvalue placement forced by unmatched disturbance and causal reference output profile are provided. Addressing nonminimum phase condition, the sliding mode controller (SMC) joins features of a conventional SMC (insensitivity to matched nonlinearities and disturbances) and a conventional dynamic compensator (accomodation to unmatched disturbances). Theoretical results are demonstrated on a numerical example.

Minimal parametrization regulators for MIMO “strict feedback form” systems

Abstract In this paper it will be considered a class of MIMO nonlinear systems in “strict feedback form” affected by a noun bounded matrix of time dependent disturbances. It will be assumed the matrix norm to be unknown, and it will be constructed a robust controller whose dynamics turn out to be minimal, yielding with this respect the best possible control strategy. It is also shown how this strategy can be applied to the elastic joint robot model simplified dynamic equations, and found a global state space coordinate transformation and a state feedback such that the system dynamics can be expressed in “strict feedback form”.

Some Applications of Soft Computing Methods in System Modeling and Control

The paper deals with the application of fuzzy systems, artificial neural networks (neural systems), and genetic algorithms to solve modeling and control problems in system engineering. Part 1 the paper covers the design of classical PID and fuzzy PID controllers for nonlinear systems with an (approximately) known dynamic model. Optimal controllers are designed based on genetic algorithms. Part 2 considers neural control of a SCARA robot. Part 3 deals with the fuzzy control of a special class of MIMO nonlinear systems and generalizes the method of Wang for such systems.

Intelligent Engineering Systems

Intelligent Engineering Systems

Adaptive Control of MIMO Non-Linear Systems Using Local ARX Models and Interpolation

A discrete-time adaptive decoupling and linearising controller is described and analysed. The model-based controller applies a particular model representation based on the combination of several simple local ARX models. The advantage of this model representation is that a minimum of system knowledge is required to determine a suitable nonlinear model structure. The class of MIMO non-linear systems considered includes systems with weak non-minimum phase effects. The analysis shows that the controller gives a globally stable closed loop with some robustness properties. A quantitative and qualitative analysis of the transient and asymptotic behavior of the control system is given. A semi-realistic simulation example illustrates some of the properties of the approach.

Direct adaptive control of a class of MIMO nonlinear systems

A direct adaptive control is presented in this paper for the control of a class of discrete-time nonlinear systems which include many useful models well known in the literature. The asymptotic stability and global convergence of the algorithm proposed in this paper have been established under mild regularity assumptions. A concept of the so-called stronger left coprime is first introduced in this paper. It is shown that the concept plays a crucial role in the problems of stabilizing a system and realizing the adaptive control algorithm.

Tracking and disturbance rejection of MIMO nonlinear systems with PI controller

We study tracking and disturbance rejection of a class of MIMO nonlinear systems with linear proportional plus integral (PI) compensator. Roughly speaking, we show that if the given nonlinear plant is exponentially stable and has a strictly increasing dc steady-state I/O map, then a simple PI compensator can be used to yield a stable unity-feedback closed-loop system which asymptotically tracks reference inputs that tend to constant vectors and asymptotically rejects disturbances that tend to constant vectors.