Research On Algorithm Design And Theory Analysis Of Double-Layer Model Predictive Control

Model predictive control is a class of computer control algorithms based on models, it manyappears in two-layer structure in industrial application, called double-layer model predictivecontrol, that is, a layer of conventional control function, based on which is an added layer ofsteady-state optimization or steady-state target calculation(SSTC). Compared with conventionalpredictive control technology, double-layer structure predictive control can deeply improve thepotential economical benefits, while keep the process operate more stable and safe. However, theabsorption of double-layer structure brings some new problems for predictive control: firstly, inthe layer of SSTC of steady-state process, the feasibility judgment and soft constraintsadjustment is the primary problem to be addressed; secondly, in the layer of SSTC of rampprocess, it is hard to optimize such process for the problem that model of steady stateoptimization cannot be formed for one-order integral process in double-layer predictive control;thirdly, the ramp objects involves security issues, so the improperly treat for the infeasibility ofSSTC will bring security risk; at last, the problem of compatibility and uniqueness for theoptimization solution rises by using conventional predictive control technology, although thecompatibility can be effectively erased by adopting the double-layer predictive control, theuniqueness can never be guaranteed.Aiming at the aforementioned problems, priority method is proposed to address thefeasibility problem of steady-state and ramp process, and then the “point” model andestablishment conditions of “critical steady state” are presented to effectively solve theoptimization problem of ramp process, at last, Starting with the causality between the steadystate of the control input and the steady state of controlled output, a steady–state relationshipbetween inputs and outputs is revealed, later an improved double-layer predictive controlsolution was given for the non-square system. The main work and results are list as follows:1) The Karush-Kuhn-Tucker (KKT) conditions for optimization problems are used toanalyze the complexity of DMC algorithm. Therefore, the number of manipulated variables and the length of control horizons are found out to be the mainly restricted two factors ofcomputational efficiency in algorithms, and the time complexity of the algorithm is proportionalto the cube of the product of the two factors. Then standard quadratic programming (QP)algorithm was applied to three classical industrial cases which simulated and verified the result.2) Aiming at the feasibility of the SSTC for the steady-state process, the SSTC ofpredictive control inherently belongs to the optimization of local linear process, so the feasibilityis a principal problem. Two-stage methods is used to solve the steady state target calculation,which means feasibility domain is obtained first and then optimized. To guarantee the existenceof feasibility domain, weighting and priority policies are presented to determine the feasibilityand adjust soft constraints. Simulation results validate the proposed approach.3) Aiming at the problem that the model of steady state optimization cannot be formed forone-order integral process in double-layer predictive control, the concept of “critical steadystate” is proposed and then the “point” model and establishment conditions of “critical steadystate”, i.e. stability condition, are presented and then build the mathematic optimization modelbased on the analysis of steady property of that process. In simulation, the presented integral typetwo-layer predictive control algorithm is implemented on a multivariable integrating process.The optimal steady state output target can be calculated and also quickly tracked by this optimalcontrol system.4) In the structure form, the multi-variable control system can be divided into three types:square system, fat system and thin system. Start with the causality between the steady state of thecontrol input and the steady state of controlled output. The output offset or the steady stateuncertainty of the control input that are produced when the thin system or fat system iscontrolled with predictive control can be boiled down to the problem of compatibility anduniqueness for non-homogeneous linear equations respectively. The reason that problem ofcompatibility and uniqueness arises is analyzed according to the criterion of solutions fornon-homogeneous linear equations and then the solutions based on the double-layer controlstructure is given. The steady state optimization can solve the compatibility problem for the thinsystem and on the other hand find the unique one from the infinite consistent solutions for the fatsystem. Simulation results validate the double-layer predictive control algorithm that presentedin this paper and the steady state solutions of the multivariable predictive control system areconsistent and unique.