Simultaneous (C, A, B)-pairs for Infinite-Dimensional Systems

The problem of robust disturbance rejection for left invertible linear systems, with nonlinear uncertain structure and with measurable and nonmeasurable disturbances, is solved via an independent from the uncertainties static measurement output feedback law. The necessary and sufficient conditions for the problem to have a solution are established. The general explicit expression of the measurement output feedback matrix and the measurement disturbances feedback matrix are derived. The feedback invariant poles are determined. Sufficient conditions for robust disturbance rejection with simultaneous robust stability are also established. The rejection of the influence of the rotary gust disturbing the vertical velocity of the longitudinal motion of an aircraft is achieved.

The problem of robust disturbance rejection for left invertible linear systems, with nonlinear uncertain structure and with measurable and nonmeasurable disturbances, is studied and solved for the first time. The necessary and sufficient conditions for the problem to have a solution, via an independent of the uncertainties static feedback law, are established. The general explicit expression of the feedback matrix is derived. The feedback invariant poles are determined. Sufficient conditions for robust disturbance rejection with simultaneous robust stability, are established.

The aim of this paper is to develop a new approach for a solution of the model following control (MFC) problem with a dynamic compensator by using linear matrix inequalities (LMIs). TheH1 model following control problem is derived following LMI formulation. First, the H1 optimal control problem is revisited by referring to Lemmas assuring all admissible controllers minimizing the H1 norm of the transfer function between the exogenous inputs and the outputs. Then, the solvability condition and a design procedure for a two degrees of freedom (2 DOF) dynamic feedback control law is introduced. The existence of a 2 DOF dynamic output feedback controller for the model following control is proven and the stability of the closed-loop system is satisfied by assuring the Hurwitz condition. The benchmark thermal process (PT-326) as the first order process with timedelay is regulated by the presented 2 DOF dynamic output feedback controller. The simulation results illustrate that the presented controller regulates a system with dead-time as a large set of generic industrial systems and the H1 norm of the closed-loop system is assured less than the H1 norm of the desired model system.

A solution is presented for the problem of diagonalization (row-by-row decoupling). The problem is solved using a constant precompensator and a dynamic output feedback compensator of a p*m linear time-invariant system. The solvability condition is compact and concerns the dimension of a single subspace defined via the concepts of essential rows and static kernels associated with the transfer matrix. A characterization of the set of all solutions to the problem is also given. In solving this dynamic feedback problem, a complete solution to its state-feedback counterpart, namely, the restricted state-feedback problem of diagonalization, is also presented. >

This paper considers dynamical compensators design for purpose of pole assignment for discrete-time linear periodic systems. Similar to linear time-invariant systems, it is pointed out that the design of a periodic dynamical compensator can be converted into the design of a periodic output feedback controller for an augmented system. Utilizing the recent result on output feedback pole assignment, parametric solutions for this problem are obtained. The design approach can be used as a basis for the robust dynamical compensator design for this type of systems. Combined with a robustness index presented in this paper, robust dynamical compensator design problem is converted into a constrainted optimization problem. A numerical example is employed to illustrate the validity and feasibility of the methods.

Dynamic Disturbance Decoupling for Discrete-Time Nonlinear Systems: A Linear Algebraic Solution

We consider the robust and perfect tracking (RPT) problem for multivariable linear systems with external disturbances. The problem is to design a proper controller such that the resulting overall closed-loop system is asymptotically stable and the controlled output almost perfectly tracks a given reference signal with an arbitrarily fast settling time in the face of external disturbances and initial conditions. We derive a set of necessary and sufficient conditions under which the RPT problem is solvable. Under these solvability conditions, we develop algorithms for constructing state and output feedback laws, explicitly parameterized in /spl epsi/, that solve the RPT problem. In our construction of feedback laws, we propose a controller structure which enables us to design a tracking controller without introducing additional integrators regardless what type the system is.

Robust Servo Problem for Decentralized Control Systems with Partial Parameter Perturbations

In this paper the robust cooperative output regulation problem for multi-agent systems (MAS) with general heterodirectional hyperbolic PIDE-ODE agents is considered. This setup also covers networks of ODEs with arbitrarily long input and output delays. The output of the agents can be defined at all boundaries, in-domain and may depend on the ODE state, while disturbances act on the agents in-domain, at the boundaries, the output and the ODE. The communication network is described by a constant digraph and if its Laplacian is reducible, then heterogeneous agents are permitted also in the nominal case. The solution is based on the cooperative internal model principle, which requires to include a diffusively driven internal model in the controller. The corresponding state feedback regulator design starts with a local backstepping stabilization of the coupled hyperbolic PIDE-ODE systems. It is shown that the remaining simultaneous stabilization of the MAS can be traced back to the simultaneous stabilization of the finite-dimensional cooperative internal model. Solvability conditions in terms of the network topology and the agents transfer behavior are presented. The new design method is applied to the formation control of a platoon of uncertain heavy ropes carrying loads to verify its applicability. Simulations confirm the synchronization performance achieved by the resulting networked controller.

While the output regulation problem for linear systems accommodates both bounded and unbounded exogenous signals, the existing formulation of the output regulation problem for nonlinear systems only allows bounded exogenous signals produced by an exosystem with a neutrally stable equilibrium. In particular, when it comes to the robust output regulation problem, the only admissible exogenous signal is a finite combination of step and sinusoidal functions. In this paper, we give a general formulation of the robust output regulation problem that admits unbounded exogenous signals, and contains the previous formulations as special cases when the system is linear or when the exogenous signals are bounded. Then, we give conditions under which the problem can be solved by solving a robust stabilization problem of an augmented system. Finally, we apply our general result to obtain the solvability conditions of the general robust output regulation problem for the class of lower triangular nonlinear systems.

The Dynamic Regulation of Linear Discrete-time Systems with Unknown Input (A Design Method Using Adaptive State Observer)

The decentralized robust servomechanism problem (DRSP) for large flexible space structures (LFSS) under sensor and actuator failures is considered. Failure conditions are modelled by failure matrices. This permits a unified treatment of sensor and actuator failures. For colocated LFSS, stabilization, tracking of constant set points, and regulating constant disturbances can be simultaneously handled using a decentralized tuning PID output-feedback controller. Necessary and sufficient conditions for solvability of the DRSP for colocated LFSS under sensor and actuator failures are derived. Two detailed examples demonstrate the effectiveness of the controller.

Mineral grinding circuit (GC) is essentially multivariable system characterized with strong couplings, large time-varying parameters and multiple time delays. The product particle size and the circulating load are two important production indexes that directly related to the operation performances of subsequent beneficiation process. However, they are usually difficult to be controlled effectively with conventional control strategies due to the above mentioned complex characteristics. Especially the various process disturbances have a great influence on the control performances of the closed-loop system. In this paper, a multivariable disturbance observer (MDOB) based analytical non-interacting control (ANC) scheme is proposed to control the complex GC with model mismatches and strong external disturbances. Control studies have been performed by simulation tests for setpoint tracking, disturbance rejection and robustness problems.

In this paper the robust asymptotic tracking and disturbance rejection problem is studied for linear periodic discrete-time systems, and for general classes of disturbance functions and reference signals, consisting in free responses of periodic processes. The necessary and sufficient conditions for the existence of a solution, which involve the periodic notion of invariant zero, are found. A constructive design procedure of the periodic compensator is given; it is based on the internal model principle.

Disturbance rejection problem solvability: From structural approach to reliability/availability analysis