Decoupling Control Schemes of Multivariable Systems Liankui DAI

Decoupling Control Schemes of Multivariable Systems (多变量系统的解耦控制) Liankui DAI, Lei XIE Institute of Industrial Control, Zhejiang University, Hangzhou, P. R. China

Tuning PID Controllers for 2*2 Interacting Systems n n n If one loop is much faster than the other one, the fast loop is tuned first with the other loop in Manual. Then the slow loop is tuned with the faster loop in Automatic. If both loops are about the same speed of response, and one variable is more important to control than the other one, detune the less important loop by setting a small gain & a long reset time. Other cases……

Problem Discussion For the controlled system, design your decoupling control systems and simulate your solution with Simu. Link. If Initial states:

Decoupler Design n n Decoupler（解耦器）Design Principle Linear Cascade Decoupler Based on Transfer Function Matrix G(s) Linear Feedforward Decoupler from G(s) Nonlinear Steady-state Cascade Decoupler Based on Basic Principles (基于过程机理 的非线性稳态解耦器)

Decoupler Design Principle Design decoupler to cancel the effects of the cross blocks, i. e. ,

Block Diagram for a General 2*2 System with Decoupler #1 Decoupling Conditions ?

Decoupler #1 for a General 2*2 System If

About Decoupler #1 Problem: (1) initial MVs’ value; (2) “Man/Auto” mode switch; (3) limit of MVs.

Block Diagram for a 2*2 System with Feedforward Decoupler

Feedforward Decoupler Design for a 2*2 System Dynamic decoupler: Steady-state decoupler: Feedforward Control & Feedforward Decoupler Existing Problems ?

Nonlinear Steady-state Complete Decoupler (全解耦器) Design principle: introduce new variables v 1, v 2 to satisfy and

Nonlinear Steady-state Triangular Decoupler (三角解耦) Design principle: introduce new variables v 1, v 2 to satisfy and

Triangular Decoupler Design for a Blending Process Steady-state model: Let

Triangular Decoupler for the Blending Process (cont. )

Complete Decoupler Design for the Blending Process Steady-state model: Let

Nonlinear Decoupler Design Example (cont. ) Steady-state model: Nonlinear decoupler:

Implementation of Nonlinear Decoupler:

Simulation of Nonlinear Decoupler for a Blending Process ( Please see …/Decoupling/Nonlinear. Decoupling. mdl )

Simulation Results of Nonlinear Decoupler

Problem Discussion There are two branches in the following pump. Please design a control system to stabilize the flow in each branch, and reduce the coupling between the branches.

Summary n n n Concept of Relative Gains Obtaining Process Gains and Relative Gain Matrix Rule of CVs and MVs Pairing Decoupling Design from Block Diagrams Decoupling Design from Basic Principles

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