On Performance Assessment For Nonlinear Control Systems Based On Minimum Variance Benchmark

Performance assessment for control systems has gotten more and more attention in re-cent years. Since the industrial process is nonlinear in nature and traditional performanceassessment methods may be unrealistic, performance assessment for nonlinear control sys-tems has been an area of active research in process control community. The key problems ofnonlinear control performance assessment are to establish the performance benchmark andestimate the white noise sequence.Generally speaking, nonlinearities in industrial processes mainly come from the equip-ment/process and actuator(valve, pump and so on). The dynamic process nonlinearities andvalve nonlinearities are usually differentiable. The valve stiction nonlinearities are staticand non-differentiable. Consider these nonlinearities, the thesis studied the minimum vari-ance performance benchmark and performance assessment methods for control systems. Themain works are listed in the following.(1) The process nonlinearity and valve nonlinearity are considered in the control system,where there is no valve stiction nonlinearity. A class of simplified Kolmogorov-Gaborpolynomial models were used to obtain the condition for the existence of minimumvariance performance benchmark. The dynamic principal component analysis wasconsidered to estimate white noise sequence. The corresponding performance assess-ment method was proposed. The simulated examples showed the effectiveness of theproposed method.(2) The process nonlinearity and valve stiction nonlinearity are considered in the controlsystem. The self-excited threshold autoregressive model was used to directly esti-mate the performance assessment benchmark and establish the performance assess-ment method. The nonlinearity can be detected by the assessment algorithm. The simulated examples and a real industrial application showed the effectiveness of theproposed method.(3) The process nonlinearity is only considered in the control system. The minimum vari-ance performance benchmark based on the fuzzy Takagi-Sugeno model was proposed.The time-varying autoregressive model was considered to estimate white noise se-quence. The performance assessment method for linear systems was extended to thatfor nonlinear systems. The simulated examples showed the effectiveness of the pro-posed method.(4) Consider the above performance assessment methods for nonlinear control systems,the control performance assessment problem was established in the tensor space. Thehigher-order singular value decomposition was used to extend the performance assess-ment method based on the minimum variance performance benchmark in the tensorspace. The simulated examples showed the effectiveness of the proposed method.