Explicit Model Predictive Control & Application In Non-linear System

Model predictive control (MPC) was used widely in the field of processes industry and gained many good social and economic benefits. But it is not suitable for high-frequency sampling or real-time systems (eg. automotive, spacecraft and so on) because of solving repetitively a computationally demanding on-line optimization.Explicit model predictive control (eMPC) overcomes the shortcoming of the model predictive control (MPC). Explicit solutions to constrained linear MPC problems can be computed by solving multi-parametric quadratic programs (mpQP), where the parameters are the components of the state vector. The solution to the mpQP is a piecewise affine (PWA) function, which can be evaluated at each sample to obtain the optimal control law. The on-line computation effort is only restricted to a table-lookup. The technique proposed in this paper is attractive for a wide range of practical problems where the computational complexity of on-line optimization is prohibitive. We can implement on the simplest, low-cost hardware, such as System On a Chip (SOC) etc.In this paper, the theory and application of eMPC was researched. The concrete content is as follows:1. Based on studied of a great deal of related literature, the research progress and general situation of the eMPC was summarized.2. The basic principles of eMPC was studied deeply. Based on the example of simulation(linear), computed the eMPC through off-line (that is computed the state partitions and the piecewise affine control law through off-line) and closed-loop simulated online. The simulation results made the theory more clearly and gained a good control performance.3. Based on the typical non-linear systems, we built their PWA model , computed the state partitions and the piecewise affine control law through off-line, looked for Piece Wise Quadratic Lyapunov function ,closed-loop simulated online ,analyzed the stability and validity of the system. 4. The technology of eMPC was applied to controlling the DC/DC Switched system .