Uncertain MIMO Systems Research Articles

Robust Adaptive Iterative Learning Control for a Generic Class of Uncertain Non-Square MIMO Systems

Robust Adaptive Iterative Learning Control for a Generic Class of Uncertain Non-Square MIMO Systems

Data-Driven Robust Finite-Iteration Learning Control for MIMO Nonrepetitive Uncertain Systems.

This work considers three main problems related to fast finite-iteration convergence (FIC), nonrepetitive uncertainty, and data-driven design. A data-driven robust finite-iteration learning control (DDRFILC) is proposed for a multiple-input-multiple-output (MIMO) nonrepetitive uncertain system. The proposed learning control has a tunable learning gain computed through the solution of a set of linear matrix inequalities (LMIs). It warrants a bounded convergence within the predesignated finite iterations. In the proposed DDRFILC, not only can the tracking error bound be determined in advance but also the convergence iteration number can be designated beforehand. To deal with nonrepetitive uncertainty, the MIMO uncertain system is reformulated as an iterative incremental linear model by defining a pseudo partitioned Jacobian matrix (PPJM), which is estimated iteratively by using a projection algorithm. Further, both the PPJM estimation and its estimation error bound are included in the LMIs to restrain their effects on the control performance. The proposed DDRFILC can guarantee both the iterative asymptotic convergence with increasing iterations and the FIC within the prespecified iteration number. Simulation results verify the proposed algorithm.

Fixed-Time Command-Filtered Adaptive Backstepping Control for a Class of Uncertain MIMO Systems

Fixed-Time Command-Filtered Adaptive Backstepping Control for a Class of Uncertain MIMO Systems

Command filter-based I&I adaptive control for MIMO uncertain systems with input saturation and disturbances

Command filter-based I&I adaptive control for MIMO uncertain systems with input saturation and disturbances

Application of Sine Cosine Egret Swarm Optimization Algorithm in Gas Turbine Cooling System

Gas turbine cooling system is a typical multivariable, strongly coupled, nonlinear, and uncertain MIMO system. In order to solve the control problem of pressure, flow, and temperature of the system, an intelligent approach is necessary and more appropriate. The current system control mainly depends on the experience of the staff, which exists problems such as high labor intensity, low work efficiency and low control accuracy. Lack of accurate models make parameters tune difficultly, and ordinary control methods are difficult to control complex gas turbine cooling system. In this paper, the system transfer function model is built based on the field data obtained under different working conditions and system identification method. The diagonal matrix decoupling method is used to weaken the correlation between variables and achieve independent control among variables. When optimizing the parameters of the controller, Sine Cosine Egret Swarm Optimization Algorithm is proposed. Egret Swarm Optimization Algorithm is composed of Sit-And-Wait strategy, random walk, and encirclement strategy. The sit-and-wait strategy is prone to premature convergence, which makes the optimized parameters unsuitable for gas turbine cooling system. Sine Cosine Algorithm is introduced to randomly use the sine-cosine function for the pseudo-gradient of the weights of the observation equation, thus expanding the search range of the population. Friedman tests prove that the deviation of SE-ESOA is within the allowable range. The results show that the result of Sine Cosine Egret Swarm Optimization Algorithm is more stable and accurate, and it is more suitable for gas turbine cooling system, which solve the pressure, flow, and temperature control problems of complex systems.

Practical tracking of MIMO uncertain stochastic systems driven by colored noises via active disturbance rejection control

Practical tracking of MIMO uncertain stochastic systems driven by colored noises via active disturbance rejection control

Performances of Uncertain LPV MIMO Metzler Systems Under PID Control

For one class of uncertain Metzler MIMO systems the concepts of matching conditions, structural parametric constraints and system positiveness is noted in this paper when solving the problem of PID control design. In particular, exploiting the supported structure of the measurement, the design task is formulated as a linear matrix inequality problem if the constraint set consistent with the controller parameter representation is found to be feasible. Covering given assumptions, action consequence of the derivative parameter of the control law is stated separate to highlight desired positiveness of the closed-loop system matrix.

Higher Order Reduction of Uncertain Systems: Affine Arithmeti

In this paper the Modified Routh Approximation (MRA) and Affine Arithmetic (AA) methods are investigates for obtaining the reduced order model (ROM) of SISO, discrete & MIMO uncertain systems into lower order system. Rigorous study and analysis of physical system direct to the outcome of systems with uncertainty instead of certain coefficients. Thus, systems having uncertain but bounded parameters known as uncertain systems are under consideration in this paper. An effective algorithm to determine the reduced order model is proposed here. This proposed methodology is verified using numerical examples available from the literature.

Event-triggered adaptive control of uncertain non-linear systems under input delay and limited resources

In this paper, both input delay and limited bandwidth challenges in uncertain networked control systems have been tackled. For this purpose, an event-triggered adaptive controller based on backstepping technique is designed for a general class of non-linear uncertain MIMO systems. The event-triggered mechanism is placed in the sensor-to-controller channel to reduce communication burden and save computational resources. Rather than predefined fixed or simple relative triggering thresholds, the proposed triggering condition is derived based on the negative semi-definiteness of derivative of Lyapunov function. To handle input delay problem, an auxiliary compensation system based on integral of input signal is introduced in the controller design. System stability are guaranteed under proposed scheme with no Zeno behavior. Simulation results on three-link cylindrical robotic arm show that the proposed control scheme successfully compensates for input delays and ensures a substantial saving in computational and network resources characterized by number of required control updates and signal transmissions over the network.

Topology-Independent Robust Stability Conditions for Uncertain MIMO Networks

We give a sufficient and a necessary condition for the topology-independent robust stability of networked systems formed by uncertain MIMO systems. Both conditions involve constants associated with the nominal node dynamics and arc interconnection matrices, the uncertainty bounds, and the maximum connectivity degree of the network; they are scalable (they can be checked locally), independent of the network topology and even of the number of nodes and arcs, and hold for networks of heterogeneous MIMO systems and interconnection matrices, with heterogeneous uncertainties. The dual cases of 1-norm and ∞-norm bounds are considered. In both cases, if the systems at the nodes are diagonal, we get a necessary and sufficient condition. We apply our results to the topologyindependent robust stability analysis of a case-study from cancer biology.

Modified backstepping algorithm for control of nonlinear systems with cross-couplings

The paper deals with an output control approach for structural uncertain MIMO systems under parametrical uncertainties, cross- reactions and external disturbances. The proposed technique ensures high quality of transients and high robustness in the steady state toward the disturbances without using high-gain components in the controller. A model transformation with one linear filter for control signal is used to obtain a structural determined form of the plant (“straight-feedback form”). The dynamical order of the filer is equal to the relative degree of MIMO plant. The procedure of relative dynamic degree estimation for nonlinear MIMO plant with cross-couplings is considered. The control algorithm combines an auxiliary loop method and backstepping method. The first one is a robust approach to unknown bounded disturbances evaluation and compensation. Backstepping is a well-known iterative procedure of control law synthesis by consecutive analysis of the plant state equations. The considered combination allows estimating undesired dynamics in each state equation and compensates it by creation of virtual control laws with equal magnitude toward disturbances and reverse sign. Experimental verification of the considered control algorithm is given with the use of a laboratory platform called “Twin Rotor MIMO System”. The platform can be controlled in two angle positions and represents the simplified helicopter dynamics.

Quantitative-fuzzy Controller Design for Multivariable Systems with Uncertainty

This work serves as a pioneer contribution in terms of application of Quantitative Feedback Theory (QFT) methodology and fuzzy logic method to design a controller for MIMO systems. Due to the presence of uncertainty in multivariable dynamic systems, the application of robust control methods for achieving high accuracy in tracking is inevitable. On the other hand, application of QFT to MIMO uncertain systems still remains to be one of the most difficult control problems for engineers. In this paper, authors attempt to simplify the MIMO control problem by proposing a new algorithm which joins QFT and fuzzy techniques. In order to illustrate the utility of the proposed algorithm, its application on a two degree of freedom link robot manipulator is depicted. Initially, a QFT controller is designed for each link to overcome the track and disturbance rejection problems. Then, a bi-level tuned PD-fuzzy controller is employed as one strategy for curbing probable errors in the previous controller. The controller design was carried in the following stages; first, a linear PD controller independently applied to each actuator. Then, fuzzy rules were developed to design a fuzzy PD controller. Fuzzy controller normalizing parameters were regulated according to maximum PD control errors. In the second stage, named nonlinear tuning, other parameters of the fuzzy controller were tuned using genetic algorithms. Finally, nonlinear simulations of arbitrary path tracking shows that the proposed controller has a consistent tracking ability, and also it can clearly be seen that the mentioned approach is precise and very simple in comparison to other MIMO control techniques.

Robust decentralized controller design based on equivalent subsystems

A method for robust decentralized controller design of continuous and discrete-time controllers for SISO and MIMO systems is proposed. The uncertain MIMO system is given by a set of square transfer matrices of any dimension. The design procedure relies on the Equivalent Subsystems Method (ESM) – an independent design of local controllers for stability and required performance of the overall system. The ESM has been extended by integrating robust stability conditions directly in the independent design of local controllers to obtain a unified robust decentralized controller design method. To demonstrate the design procedure, a discrete-time robust decentralized PID controller for a minimum-phase system was designed.

Observer-based fractional-order adaptive type-2 fuzzy backstepping control of uncertain nonlinear MIMO systems with unknown dead-zone

A new problem of observer-based fractional adaptive type-2 fuzzy backstepping control for a class of fractional-order MIMO nonlinear dynamic systems with dead-zone input nonlinearity is considered in the presence of model uncertainties and external disturbances where the control scheme is constructed by combining the backstepping dynamic surface control (DSC) and fractional adaptive type-2 fuzzy technique. First, a linear state observer estimates immeasurable states. Second, the unknown nonlinear functions of the uncertain system are approximated with interval type-2 fuzzy logic systems. Third, to avoid the complication of backstepping design process, the DSC is used. Fourth, by using the fractional adaptive backstepping, fractional adaptive laws are constructed, the proposed method is applied to a class of uncertain fractional-order nonlinear MIMO system. In order to have a better control performance in reducing tracking error, the controller parameters are tuned by using the PSO algorithm. Stability of the system is proven by the Mittag-Leffler method. It is presented that the proposed design guarantees the boundedness property for the system and also the tracking error can converge to a small neighborhood of the zero. The simulation examples are given to show the efficiency of the proposed controller.

Adaptive backstepping control for a class of MIMO uncertain underactuated systems with input constraints

Adaptive backstepping control for a class of MIMO uncertain underactuated systems with input constraints

Dynamic Compensator-Based Output Feedback Controller Design for Uncertain Systems with Adjustable Robustness

A low-order dynamics compensator-based output feedback stabilization method for a class of uncertain linear MIMO systems with mismatched disturbances is presented. Since all the system states are not measurable, the proposed controller inherently has low-pass filter property in which it can successfully replace the derivative terms of the system output and hence effectively estimate the input disturbance. The control scheme proposed here can simultaneously consider the input saturation problem and obtain the desired performance. Although the system has unknown uncertainties and disturbances, the uniformly ultimate boundedness of system states in the closed-loop system is analytically shown using the Lyapunov method. Finally, two numerical examples are presented to demonstrate the applicability of the proposed scheme.

Pseudo-PID Robust Tracking Design Method for a Significant Class of Uncertain MIMO Systems

In this paper, for a significant class of uncertain MIMO systems, in particular for robots, new fundamental results are stated. These allow to design robust control laws without chattering, of pseudo-PID type, in order to track sufficiently regular trajectories with a preassigned maximum error. The proposed pseudo-PID controllers are easy to design and implement because these laws can also be decentralized and they are based on two design parameters. The first parameter is related to the minimum eigenvalue of a suitable matrix, depending on the inertia matrix in the case of a mechanical system, from which the practical stability depends on, and the second parameter is related to the practical region of asymptotic stability, to the precision of the tracking error and to the time constant of an appropriate linearized majorant system of the closed-loop control system. The utility and the efficiency of the main results proposed in this paper are illustrated with a significant example.

Adaptive robust fault tolerant control design for a class of nonlinear uncertain MIMO systems with quantization

In this paper, we investigate the adaptive control problem for a class of nonlinear uncertain MIMO systems with actuator faults and quantization effects. Under some mild conditions, an adaptive robust fault-tolerant control is developed to compensate the affects of uncertainties, actuator failures and errors caused by quantization, and a range of the parameters for these quantizers is established. Furthermore, a Lyapunov-like approach is adopted to demonstrate that the ultimately uniformly bounded output tracking error is guaranteed by the controller, and the signals of the closed-loop system are ensured to be bounded, even in the presence of at most m−q actuators stuck or outage. Finally, numerical simulations are provided to verify and illustrate the effectiveness of the proposed adaptive schemes.

An optimal adaptive robust PID controller subject to fuzzy rules and sliding modes for MIMO uncertain chaotic systems

In this paper, an optimal adaptive robust PID controller based on fuzzy rules and sliding modes is introduced to present a general scheme to control MIMO uncertain chaotic nonlinear systems. In this control scheme, the gains of the PID controller are updated by using an adaptive mechanism, fuzzy rules, the gradient search method, and the chain rule of differentiation in order to minimize the sliding surfaces of sliding mode control. More precisely, sliding mode control is used as a supervisory controller to provide sufficient control inputs and guarantee the stability of the control approach. To ascertain the parameters of the proposed controller and avoid trial and error, the multi-objective genetic algorithm is employed to augment the performance of proposed controller. The chaotic system of a Duffing-Holmes oscillator and an industrial robotic manipulator are the case studies to evaluate the performance of the proposed control approach. The obtained results of this study regarding both systems are compared with the outcomes of two notable studies in the literature. The results and analysis prove the efficiency of the proposed controller with regard to MIMO uncertain systems having challenging external disturbances in terms of stability, minimum tracking error and optimal control inputs.

Adaptive Fault Tolerant Stabilization for Uncertain MIMO Systems with Actuation Failures

This paper considers the state stabilization problem for a class of non-affine uncertain MIMO systems with actuation failures. An adaptive robust fault-tolerant control is developed to compensate the affect of uncertainties, actuator failures. And theoretical analysis based on a Lyapunov-like approach demonstrates that, under some proper conditions, the close-loop system would be stabilized and ultimately uniformly bounded state error could be guaranteed by the controller. Further, the proposed controller is no need for on-line fault detection and diagnosis unit, and inexpensive to compute. At last, numerical simulations are provided to validate and illustrate the benefits and effectiveness of the proposed control scheme.