Decoupling Control Schemes of Multivariable Systems ( 多变量系统的解耦控制 ) Dai Lian-Kui Shen Guo-jiang Institute of Industrial Control, Zhejiang University

Last Lecture Definition of Relative Gain Calculation of Relative Gain Meaning of Relative Gain Matrix Calculation of Relative Gain Matrix CVs and MVs Pairing

Problems of Multivariable Process Which is the best pairing of controlled and manipulated variables? How does the interaction affect the stability of the loops? How should the feedback controllers be tuned in a multivariable scheme? Can something be done with the control scheme to break, or minimize, the interaction between loops?

Interaction and Stability Characteristic equations for loop 2(No.1 controller are in “M” model ): Characteristic equations for loop 1(No.2 controller are in “M” model ): Characteristic equations for complete system( both controllers are in “A” mode):

Interaction and Stability (cont.) The roots of the characteristic equation for each individual loop are not the roots of the characteristic equation for the complete system. For interaction to affect the stability, it must work both ways. The interaction effect on one loop can be eliminated by interrupting the other loop; this is easily done by switching the controller to manual.

Tuning PID Controllers for 2*2 Interacting Systems 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……

Content When Necessary to Design Decoupler Linear Decoupler Design from Block Diagrams Nonlinear Decoupler Design from Basic Principles Application Examples

Pairing Example of a Blending Process Steady-state model: Problem: how can you analyze the coupling between two loop ?

Pairing of a Blending Process (cont.) 1. Obtaining steady-state process gain:

Pairing of a Blending Process (cont.) 2. Obtaining relative gain matrix:

Pairing of a Blending Process (cont.) 3. Pairing CVs and MVs using RGM If F 1 >F 2, the correct pairing is F － F 1, C － F 2 ; If F 2 >F 1, the correct pairing is F － F 2, C － F 1. If F 2 =F 1, which is the correct pairing ?

When necessary to apply decoupling for a coupling process (1) Strong interaction exists （存在强耦合） : even for the best pairing option, one or more of the relative gains is far from unity, (2) Both loops are about the same speed of response, and both CVs are of the same important （两回路动态特性接近，且两被控 变量均同等重要）.

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

Decoupler Design 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 Cascade Decoupler Decoupling Conditions ?

Cascade Decoupler for a General 2*2 System If

About Cascade Decoupler Problem: (1) initial MVs’ value or “Man/Auto” mode switch; (2) 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 Decoupler:

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