Research On Offset-free Model Predictive Control For Mixed Uncertain Systems

The success of Model Predictive Control in complex industrial processes over the years has fully demonstrated its enormous potential for dealing with complex constrained optimal control problems.With the development of science,technology and human society,model predictive control is widely used in the fields of energy,automobiles,and unmanned aerial vehicle.These fields are more sensitive to system noises,requiring the controller to achieve the control target while minimizing conservativeness caused by handling noises.This paper expands from the control problem when deterministic noise,stochastic noise and model mismatch appear in the systems and gets the following achievements:· As for offset-free tracking for uncertain systems,this paper presents a linear mismatched model based offset-free MPC approach for nonlinear systems(also suits for mismatched linear systems)with both bounded stochastic and deterministic disturbances.By treating the objective function(using disturbance observer model)and the constraints(using mismatched predictive model)individually,offset-free tracking for piece-wise constant references in an expectation manner and constraints contentment has been achieved.A com-bined state and disturbance-affine feedback control law has been incorporated to achieve least conservativeness.Well designed invariant set for tracking is used for convergence.An iterative computation procedure has been proposed to find the recursively feasible set which ensures recursive feasibility.The final Optimal Control Problem(OCP)has been converted to a Semidefinite Programming(SDP)problem which can be efficiently solved by existed solvers.The proposed method has been applied to a nonlinear Continuously Stirred Tank Reactor(CSTR)system and the performance has been compared to several existing approaches.· As for computing the feasible set,this paper proposes a multi-parametric programming based algorithm to compute the feasible set for OCP derived from MPC-based algorithms and involving both spectrahedron(represented by linear matrix inequalities)and polyhedral(represented by a set of inequalities)constraints.According to the geometrical meaning of inner product of vectors,the maximum length of the projection vector from the feasible set to a unit spherical coordinates vector is computed and the optimal solution has been proved to be one of the vertices of the feasible set.After computing all the vertices,the convex hull of these vertices is computed which equals to the feasible set.The simulation results show that the proposed method is especially efficient for low dimensional feasible set computation and avoids non-unicity problem of optimizers as well as the memory consumption problem that encountered by projection algorithms.· As for constrains design,with regard to non-square uncertain systems,this paper proposes an output constrains design approach in steady-state target calculation stage of the double layered model predictive control by making use of system operability and interval control.Output constrains designed by this method guarantees the feasibility of MPC controller when doing steady-state target calculation and makes the system operating point work at the economic optimum.Meanwhile,this paper presents a test method for feasibility of steady-state target calculation of non-square uncertain system.The application to examples from low dimension to high dimension proves the design approach and test method to be available and efficient.