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Control Loop Interactions

Introduction. We have focused on single-input, single-output (SISO) control problemsMost real control problems involve multiple inputs and multiple outputs (MIMO)Each input usually affects multiple outputsCan be difficult to design and tune control systemMultiloop control strategyPair input and

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Control Loop Interactions

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    1. Control Loop Interactions Introduction Multivariable systems Controller interactions Multivariable closed-loop stability Simulink example

    2. Introduction We have focused on single-input, single-output (SISO) control problems Most real control problems involve multiple inputs and multiple outputs (MIMO) Each input usually affects multiple outputs Can be difficult to design and tune control system Multiloop control strategy Pair input and output variables together Design SISO controller for each input/output pair Attempt to minimize interactions between controllers

    3. Multivariable Systems Blending system wA and wB affect both w and x Not clear how to pair variables Distillation column Pair R/xD and S/xB Significant interactions between controllers Flash drum Pair G/P and L/h Main interactions will be G on h

    4. Stirred Tank Heating Example Control problem Manipulated inputs: wh and wc Controlled outputs: T and h Mass and energy balances Simplify energy balance using product rule

    5. Stirred Tank Heating Example cont. Take Laplace transform and simplify Transfer function matrix representation

    6. Transfer Function Matrices 2x2 systems nxn systems

    7. Multiloop Control Schemes for 2x2 Systems

    8. Controller Interactions Suppose a disturbance causes Y1 to deviate from its setpoint Ysp1 Gc1 will respond to non-zero error E1 by changing U1 to drive Y1 to Ysp1 Change in U1 will also cause Y2 to deviate from its setpoint Ysp2 Gc2 will respond to non-zero error E2 by changing U2 to drive Y2 to Ysp2 Change in U2 will also cause Y1 to deviate from its setpoint Ysp1

    9. Controller Interaction Analysis Second controller in manual (Gc2 = 0) This is the transfer function used to design Gc1 Second controller in automatic (Gc2 non-zero) This is not the transfer function used to design Gc1 The effective transfer function depends on Gc2 Cannot tune the two controllers independently

    10. Controller Interaction Example Distillation column model SISO controller tuning R/xD: Kc = 0.604, tI = 16.3 S/xB: Kc = -0.127, tI = 14.46

    11. Multivariable Closed-Loop Stability Closed-loop relations for 1-1/2-2 control scheme Closed-loop characteristic equation Stability depends on both controllers in a complex way If Gp12 = 0 or Gp21 = 0 then stability depends only on the stability of the two individual control loops

    12. Closed-Loop Stability Example Transfer function model Proportional controllers Characteristic equation for 1-1/2-2 scheme

    13. Simulink Example Transfer function model 1/1-2/2 IMC controller design (tc = 5)

    14. Simulink Model

    15. SISO Control Systems

    16. MIMO Control System

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