Integrated Control Problem Research Articles

On generalization of integral control to a class of nonlinear uncertain systems

Abstract The paper is concerned with some new view on the problem of integral control in the context of nonlinear uncertain systems. There is demonstrated that a standard integral action, applied to linear control system with so-called load disturbances, can be generalized to comprise a class of linearly parametrized nonlinear SISO systems with functional uncertainty. In the last case the integral action turned out to be in fact an adaptation law of unknown parameters. It has been found that the obtained proportional-integral controller's variable gains are in fact the basis functions of the system unknown nonlinearity approximator.

On Generalization of Integral Control to a Class of Nonlinear Uncertain Systems

The paper is concerned with some new view on the problem of integral control in the context of nonlinear uncertain systems. There is demonstrated that a standard integral action, applied to linear control system with so-called load disturbances, can be generalized to comprise a class of linearly parametrized nonlinear SISO systems with functional uncertainty. In the last case the integral action turned out to be in fact an adaptation law of unknown parameters. It has been found that the obtained proportional-integral controller's variable gains are in fact the basis functions of the system unknown nonlinearity approximator.

Impact modeling and control for industrial manipulators

The impact-force behavior is experimentally studied on a 6-DOF commercial manipulator interacting with a very hard granite surface. It is shown that the elastic-joint robot model proposed by Spong (1987) completely explains frequency and damping of impact-force oscillations, so that oscillations can be totally ascribed to joint compliance, while links behave as rigid bodies. This article shows, through analysis and experiments, how to effectively employ integral control even in the transition phase, maintaining contact with the environment without bounce despite the potential problems of integrator wind-up. We begin by describing the experimental setup and how the manipulator model is derived. We then report the experimental results and model validation and discuss the open-loop permanent contact and impact. We also give an analysis of the wind-up problem of integral control, propose methods to avoid or counteract it, and report bounceless experimental controlled impacts.

Multihorizon Operative Control of Electric Power System

A operative integrated control problem of electric power system is formulated as the problem of operative control of: electric energy production processes, electric energy distribution processes and maintenance processes of electric systems elements. It is a mixed management - control problem. Multihorizon control method is applied for the problem solution. In this method the primary problem is substituted by a sequence(q = N-1, N-2,…,1,0) of N optimization subproblems each being defined for its own partial time horizon Tq(e.g. one year, three months, one month, one week, one day, “zero”). The q-th optimization sub-problem is connected with q+1 -th optimization subproblem (where Tq < Tq+1) by final state conditions X¯qto+Tq=X¯q+1to+Tq. The solution sequence is started with q=N-1-th subproblem. The state vector of the system X¯ has the components: inventories of fuels at each thermal power plant, state of maintenance processes realization at each element of the system, wear indices of each element of the system.

Modeling large power systems for efficient load frequency control

The problem of optimal proportional plus integral control of large power systems subject to stochastic load variations is discussed. It is proposed to employ a simplified observable canonical state variable model in order to reduce the computational burden of the control algorithm. The number of major computer operations involved in the conventional Riccati equation-based algorithm as also in the recently proposed Chandrasekhar equation-based algorithm is shown to be significantly reduced if the proposed canonical model is employed. Numerical results for a two-area system are also presented for which the canonical model is shown to have the additional advantage of permitting decentralized implementation of the optimal control.

Optimal Control of Stochastic Integrals and Hamilton–Jacobi–Bellman Equations. I

We consider the solution of a stochastic integral control problem and we study its regularity. In particular, we characterize the optimal cost as the maximum solution of \[\begin{gathered} \forall v \in V,\quad A(v)u \leqq f(v)\quad {\text{in }}\mathcal{D}'(\mathcal{O}), \hfill \\ u = 0\quad {\text{on }}\partial \mathcal{O},\quad u \in W^{1,\infty } (\mathcal{O}), \hfill \\ \end{gathered} \] where $A(v)$ is a uniformly elliptic second order operator and V is the set of the values of the control.

Optimal Control of Stochastic Integrals and Hamilton–Jacobi–Bellman Equations. II

We consider the solution of a stochastic integral control problem and we study its regularity. In particular, we characterize the optimal cost as the maximum solution of \[\begin{gathered} \forall v \in V,\quad A(v)u \leqq f(v)\quad {\text{in }}\mathcal{D}'(\mathcal{O}), \hfill \\ u = 0\quad {\text{on }}\partial \mathcal{O},\quad u \in W^{1,\infty } (\mathcal{O}), \hfill \\ \end{gathered} \] where $A(v)$ is a uniformly elliptic second order operator and V is the set of the values of the control.

Sufficiency conditions for multiple integral control problems

The construction of multiple integrals which are independent, in the sense that they depend solely on the values of their integrands on the boundary of the domain of integration is described. These integrals are applied to the derivation of a sufficiency condition for multiple integral optimal control problems.