Robust decentralized H_∞ control of multi-channel systems with norm-bounded parametric uncertainties

A robust decentralized H∞ control problem for uncertain multi-channel systems is considered. The uncertainties are assumed to be time-invariant, norm-bounded, and exist in both the system and control input matrices. The dynamic output feedback is mainly dealt with. A necessary and sufficient condition for the uncertain multi-channel system to be stabilized robustly with a specified disturbance attenuation level is derived based on the bounded real lemma, which is reduced to a feasibility problem of a nonlinear matrix inequality （NMI）. A two-stage homotopy method is used to solve the NMI iteratively. First, a decentralized controller for the nominal system with no uncertainty is computed by imposing structural constraints on the coefficient matrices of the controller gradually. Then the decentralized controller is modified, again gradually, to cope with the uncertainties. On each stage, a variable is fixed alternately at the iterations to reduce the NMI to a linear matrix inequality （LMI）. A given example shows the efficiency of this method.

Design of decentralized robust H_∞ state feedback controller

The design of decentralized robust H_∞ state feedback controller for large-scale interconnected systems with value bounded uncertainties existing in the state, control input and interconnected matrices was investigated. Based on the bounded real lemma a sufficient condition for the existence of a decentralized robust H_∞ state feedback controller was derived. This condition is expressed as the feasibility problem of a certain nonlinear matrix inequality. The controller, which makes the closed-loop large-scale system robust stable and satisfies the given H_∞ performance, is obtained by the offered homotopy iterative linear matrix inequality method. A numerical example is given to demonstrate the effectiveness of the proposed method.

Decentralized Robust Control for Large Scale Interconnected Uncertain Systems with Time delay

For a class of interconnected time delay uncertain systems satisfing the matching conditions, the sufficient condition for decentralized stabilization feedback control laws is derived based on Lyapunov stability theorem. This condition is expressed as the solvability problem of linear matrix inequalities(LMI). It can be easily determined whether or not, it is feasible and one can easily obtain the decentralized stabilizing state feedback matrices via LMI techniques. The method overcomes the limitations of the existing algebraic Riccati equation method. The given example shows the application of the method.

Decentralized H_∞ state feedback control for large-scale interconnected uncertain systems with multiple delays

Decentralized H_∞ control was studied for a class of interconnected uncertain systems with multiple delays in the state and control and time varying but norm-bounded parametric uncertainties. A sufficient condition which makes the closed-loop system decentralized asymptotically stable with H_∞ performance was derived based on Lyapunov stability theorem. This condition is expressed as the solvability problem of linear matrix inequalities. The method overcomes the limitations of the existing algebraic Riccati equation method. Finally, a numerical example was given to demonstrate the design procedure for the decentralized H_∞ state feedback controller.

STATE SPACE METHODS FOR DECENTRALIZED H_∞ CONTROL

This paper presents state space methods for decentralized Hoe control, which contain two respects: a parametrization approach and an iterative algorithm. For large scale systems with N subsystems, decentralized Hoe con trollers can be derived by a parametrization result for centralized Her: controllers and designed by an iterative algorithm with structured constraint to the controllers.

Design of decentralized robust stabilizing controller for interconnected time-varying uncertain systems

For interconnected uncertain systems which are time-varying and assumed to satisfy the matching conditions, a sufficient condition for decentralized stabilization feedback control laws is derived. This condition is expressed as the solvability problem of linear matrix inequalities (LMIs). Based on that, a convex optimization problem with linear matrix inequality (LMI) constraints is formulated to design a decentralized state feedback controI with smaller gain parameters which enables the closed-loop system asymptotically stable.

MODAL SYNTHESIS METHOD FOR NORM COMPUTATION OF H_∞ DECENTRALIZED CONTROL SYSTEMS (II)

When using H_∞ techniques to design decentralized controllers for large systems, the whole system is divided into subsystems, which are analysed using H_∞ control theory before being recombined. An analogy was established with substructural analysis in structural mechanics, in which H_∞ decentralized control theory corresponds to substructural modal synthesis theory so that the optimal H_∞ norm of the whole system corresponds to the fundamental vibration frequency of the whole structure. Hence, modal synthesis methodology and the extended Wittrick_Williams algorithm were transplanted from structural mechanics to compute the optimal H_∞ norm of the control system. The orthogonality and the expansion theorem of eigenfunctions of the subsystems H_∞ control are presented in part (Ⅰ) of the paper. The modal synthesis method for computation of the optimal H_∞ norm of decentralized control systems and numerical examples are presented in part (Ⅱ).

Design of a Robust Optimal Decentralized PI Controller Based on Nonlinear Constraint Optimization For Level Regulation: An Experimental Study

This paper presents the development of a new robust optimal decentralized PI controller based on nonlinear optimization for liquid level control in a coupled tank system. The proposed controller maximizes the closed-loop bandwidth for specified gain and phase margins, with constraints on the overshoot ratio to achieve both closed-loop performance and robustness. In the proposed work, a frequency response fitting model reduction technique is initially employed to obtain a first order plus dead time(FOPDT) model of each higher order subsystem. Furthermore, based on the reduced order model, a proposed controller is designed. The stability and performance of the proposed controller are verified by considering multiplicative input and output uncertainties. The performance of the proposed optimal robust decentralized control scheme has been compared with that of a decentralized PI controller. The proposed controller is implemented in real-time on a coupled tank system. From the obtained results,it is shown that the proposed optimal decentralized PI controller exhibits superior control performance to maintain the desired level, for both the nominal as well as the perturbed case as compared to a decentralized PI controller.

A Decentralized Autonomous Control on Highly Redundant Robot Manipulators

The control method of highly redundant robot manipulators is introduced. A decentralized autonomous control scheme is used to guide the movement of robot manipulators so that the work done by manipulators is minimized. The method of computing pseudoinverse which needs too many complicated calculation can be avoided. Then the calculation and control of robots are simplified. At the same time system robustness/fault tolerance is achieved.

Robust H_∞ control for neutral stochastic uncertain systems with time-varying delay

The problem of robust H_∞ control for uncertain neutral stochastic systems with time-varying delay is discussed.The parameter uncertaintie is assumed to be time varying norm-bounded.First,the stochastic robust stabilization of the stochastic system without disturbance input is investigated by nonlinear matrix inequality method.Then,a full-order stochastic dynamic output feedback controller is designed by solving a bilinear matrix inequality（BMI）,which ensures a prescribed stochastic robust H_∞ performance level for the resulting closed-loop system with nonzero disturbance input and for all admissible uncertainties.An illustrative example is provided to show the feasibility of the controller and the potential of the proposed technique.

Robustness-tracking control based on sliding mode and H_∞ theory for linear servo system

A robustness-tracking control scheme based on combining H_∞ robust control and sliding mode control is proposed for a direct drive AC permanent-magnet linear motor servo system to solve the conflict between tracking and robustness of the linear servo system. The sliding mode tracking controller is designed to ensure the system has a fast tracking characteristic to the command, and the H_∞ robustness controller suppresses the disturbances well within the close loop(including the load and the end effect force of linear motor etc.) and effectively minimizes the chattering of sliding mode control which influences the steady state performance of the system. Simulation results show that this control scheme enhances the track-command-ability and the robustness of the linear servo system, and in addition, it has a strong robustness to parameter variations and resistance disturbances.

DECENTRALIZED H_∞ SUBOPTIMAL DESIGN:AN LMI APPROACH

Address the design of state feedback H ∞ suboptimal controllers. Through parameterization of decentralized controllers, the design condition for the feedback gain is given in the form of a biaffine matrix inequality. An iterative algorithm based on linear matrix inequality(LMI) is proposed to obtain the decentralized controller which ensures the closed loop system asymptotically stable and the H ∞ norm less than constant number 1.

Robust State Feedback H_∞Control for Dynamic Biped Robot Based on T-S Fuzzy Model

T-S fuzzy model was applied to describe nonlinear system and global fuzzy model was expressed by the form of uncertain system.Based on robust state feedback H_∞control strategy,designed a global asymptotic steady fuzzy model.This control system can use the experimental input-output data pairs for the biped robot learning and walking with dynamic balance.It is proved by simulation result that robust state feedback H_∞control method based on T-S fuzzy model can effectively restrain the effect of model uncertainties and external disturbance acting on biped robot.From these works,we showed the satisfactory performance of joint tracking without any chattering.

Output Feedback Robust H_(∞) Control for Discrete 2D Switched Systems

The two-dimensional(2-D)system has a wide range of applications in different fields,including satellite meteorological maps,process control,and digital filtering.Therefore,the research on the stability of 2-D systems is of great significance.Considering that multiple systems exist in switching and alternating work in the actual production process,but the system itself often has external perturbation and interference.To solve the above problems,this paper investigates the output feedback robust H_(∞)stabilization for a class of discrete-time 2-D switched systems,which the Roesser model with uncertainties represents.First,sufficient conditions for exponential stability are derived via the average dwell time method,when the system’s interference and external input are zero.Furthermore,in the case of introducing the external interference,the weighted robust H_(∞)disturbance attenuation performance of the underlying system is further analyzed.An output feedback controller is then proposed to guarantee that the resulting closed-loop system is exponentially stable and has a prescribed disturbance attenuation levelγ.All theorems mentioned in the article will also be given in the form of linear matrix inequalities(LMI).Finally,a numerical example is given,which takes two uncertain values respectively and solves the output feedback controller’s parameters by the theorem proposed in the paper.According to the required controller parameter values,the validity of the theorem proposed in the article is compared and verified by simulation.

Augmented Lagrangian Genetic Algorithm Based Decentralized Control Configuration Design for Fluid Catalytic Cracking Units

In this work, three decentralized control configuration designs—independent, sequential and simultaneous designs—were used in multivariable feedback configurations for PI control of the riser and regenerator temperatures of FCCU in order to compare their performances. Control design was formulated as optimization problem to minimize infinity norm of weighted sensitivity functions subject to μ-interaction measure bound on diagonal complementary functions of the closed loop system. The optimization problem was solved using augmented Lagrangian genetic algorithm. Simulation results show that simultaneous and independent designs give good response with less overshoot and with no oscillation. Bound on μ-interaction measure is satisfied for both designs meaning that their nominal stabilities are guaranteed;however, it is marginal for simultaneous design. Simultaneous design outperforms independent design in term of robust performance while independent design gives the best performance in terms of robust stability. Sequential design gives the worst performance out of the three designs.

Reduced-order design of Robust H_∞ Controller for an Inertial Stabilized Aerial Platform

The uncertainty disturbance is one of the main disturbances that seriously influences the stabilization precision of an aerial inertially stabilized platform(ISP)system.In this paper,to improve the stabilization precision of the ISP under disturbance uncertainty,a robust H∞controller is designed in this paper.Then,the reduction order is carried out for high-order controllers generated by the robust H∞loop shaping control method.The application of the minimum implementation and balanced truncation algorithm in controller reduction is discussed.First,the principle of reduced order of minimum implementation and balanced truncation are analyzed.Then,the method is used to reduce the order of the high-order robust H∞loop shaping controller.Finally,the method is analyzed and verified by the simulations and experiments.The results show that by the reduced-order method of minimum implementation and balanced truncation,the stabilization precision of the robust H∞loop shaping controller is increased by about 10%.

Robust Control Design of Wheeled Inverted Pendulum Assistant Robot

This paper examines the design concept and mobile control strategy of the human assistant robot I-PENTAR(inverted pendulum type assistant robot). The motion equation is derived considering the non-holonomic constraint of the twowheeled mobile robot. Different optimal control approaches are applied to a linearized model of I-PENTAR. These include linear quadratic regulator(LQR), linear quadratic Gaussian control(LQG), H_2 control and H_∞ control. Simulation is performed for all the approaches yielding good performance results.

Generalized Internal Model Robust Control for Active Front Steering Intervention

Because of the tire nonlinearity and vehicle＇s parameters＇uncertainties,robust control methods based on the worst cases,such as H_∞,μsynthesis,have been widely used in active front steering control,however,in order to guarantee the stability of active front steering system（AFS）controller,the robust control is at the cost of performance so that the robust controller is a little conservative and has low performance for AFS control.In this paper,a generalized internal model robust control（GIMC）that can overcome the contradiction between performance and stability is used in the AFS control.In GIMC,the Youla parameterization is used in an improved way.And GIMC controller includes two sections：a high performance controller designed for the nominal vehicle model and a robust controller compensating the vehicle parameters＇uncertainties and some external disturbances.Simulations of double lane change（DLC）maneuver and that of braking on split-μroad are conducted to compare the performance and stability of the GIMC control,the nominal performance PID controller and the H_∞controller.Simulation results show that the high nominal performance PID controller will be unstable under some extreme situations because of large vehicle＇s parameters variations,H_∞controller is conservative so that the performance is a little low,and only the GIMC controller overcomes the contradiction between performance and robustness,which can both ensure the stability of the AFS controller and guarantee the high performance of the AFS controller.Therefore,the GIMC method proposed for AFS can overcome some disadvantages of control methods used by current AFS system,that is,can solve the instability of PID or LQP control methods and the low performance of the standard H_∞controller.

H_∞ Preview Control for Automatic Carrier Landing

This paper focuses on the application of H_∞preview control in automatic carrier landing system(ACLS)for carrier-based aircraft.Due to the mutual movement between aircraft and carrier,the landing process becomes considerably more challenging compared to a conventional runway landing.ACLS systems mitigate this by predicting deck motion and generating ideal glide slope path for tracking.Although,this predicted glide slope information is available in advance,conventional control structures are still unable to use this future information.H_∞preview control has the ability to utilize this future information for improving tracking response and disturbance rejection.The process of incorporating preview information into ACLS framework and synthesizing the H_∞preview controller is presented.The methodology is verified using the example of F/A-18 automatic carrier landing problem and results are presented.

H_∞ ROBUST PERFORMANCE DESIGN FOR UNCERTAIN SYSTEMS

This paper considers the robust per formance design problem of the linear systems with both unmodelled dynamics and real parametric uncertainties. We suggest for the first time that the problem can besolved by the H∞ mixed sensitivity method. The main idea is as follows: Firstly, the original problem istransformed into the robust per formance design problem for a pure parameter uncertain system. Then, theresulting problem is reduced to a standard H∞ control problem which can be solved by the H∞ state feedbacksynthesis method or Doyle’s "DGKF" algorithm.