Steady-State Gain Identification and Control of Multivariable Unstable Systems

Static gain estimation for nonlinear dynamic systems from steady-state values hidden in historical data

Static gains are often required for control, diagnosis and optimization of nonlinear dynamic systems. This paper proposes a new approach to estimate static gains for nonlinear dynamic systems from steady-state values hidden in historical data. First, steady-state values of system inputs and outputs are extracted by automatically finding data segments in steady-state conditions. Second, static gains of nonlinear dynamic systems in different operating conditions are estimated via linear regression from these steady-state values. The proposed approach has two practical features: (i) estimated static gains can be verified in a convincing way, because the validness of extracted steady-state values is confirmed by visualizing data segments in steady-state conditions, and the accuracy of estimated static gains is verified by comparing the extracted steady-state values and their estimates; (ii) the proposed approach is simple to understand and implement in practice, since it only involves a linear equation between steady-state values and static gains, as well as a basic technique of linear regression. Numerical simulation and industrial application demonstrate the effectiveness of the proposed approach.

SSGM Based Multivariable Control of Unstable Non-Square Systems

Davison (1976) proposed a method to design controllers for multivariable systems using the knowledge of only the Steady-State Gain Matrix (SSGM) of the system. In the present work, Davison's method is suitably modified to design controllers for unstable non-square multivariable systems. A single-stage multivariable PI controller is designed using the SSGM. Simulation results show that the overshoots of the closed loop responses are larger, hence a two-stage P-PI control system is proposed. For the proposed two- stage design (i) the system is first stabilized by a simple proportional controller matrix designed based on SSGM using modified Davison's method (1976). (ii) Diagonal PI controllers are designed for this stabilized system based on gain matrix. Simulation studies are carried out to compare the closed loop performance of the single stage multivariable PI control system with that of the two-stage control system (inner loop centralized P controllers and outer loop diagonal PI controllers). A method to identify the steady state gain matrix of a non-square multivariable (SSGM) unstable system under closed loop control is presented. The effect of disturbances and measurement noise on the identification of SSGM is also discussed.

Simple method of designing centralized PI controllers for multivariable systems based on SSGM

A method is given to design multivariable PI/PID controllers for stable and unstable multivariable systems. The method needs only the steady state gain matrix (SSGM). The method is based on the static decoupler design followed by SISO PI/PID controllers design and combining the resulted decoupler and the diagonal PI(D) controllers as the centralized controllers. The result of the present method is shown to be equivalent to the empirical method proposed by Davison EJ. Multivariable tuning regulators: the feed-forward and robust control of general servo-mechanism problem. IEEE Trans Autom Control 1976;21:35-41. Three simulation examples are given. The performance of the controllers is compared with that of the reported centralized controller based on the multivariable transfer function matrix.