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Loop Shaping

Design controllers to shape open-loop frequency response of SISO or MIMO feedback control system

In loop-shaping controller synthesis, you specify the shape of the open-loop response you want, and use a loop-shaping function to compute a controller that approximates that shape.

Most controller designs involve a tradeoff between performance and robustness against uncertainty. Robust Control Toolbox™ commands for loop-shaping controller design let you determine the tradeoff that best meets the requirements of your system. loopsyn lets you adjust the balance between performance and robustness. ncfsyn focuses on robust stability, while mixsyn focuses on performance.


loopsynLoop-shaping controller design with tradeoff between performance and robustness
ncfsynLoop shaping design using Glover-McFarlane method
mixsynMixed-sensitivity H synthesis method for robust control loop-shaping design
makeweightWeighting function with monotonic gain profile
mkfilterGenerate Bessel, Butterworth, Chebyshev, or RC filter
augwPlant augmentation for weighted mixed-sensitivity H and H2 loop-shaping design


  • Loop Shaping for Performance and Robustness

    Loop shaping is an approach to control design in which you determine a suitable profile for the open-loop system response and design a controller to achieve that shape.

  • Loop-Shaping Controller Design

    Compute a controller for a MIMO model of an aircraft using loopsyn. Adjust the balance between performance and robustness to obtain satisfactory responses while avoiding fragile designs.

  • Mixed-Sensitivity Loop Shaping

    Mixed-sensitivity loop shaping combines specifications for both performance and stability into one cost function that penalizes both sensitivity and complementary sensitivity.

  • Loop Shaping Using the Glover-McFarlane Method

    Use ncfsyn to shape the open-loop response while enforcing stability and maximizing robustness.