A controller design strategy for nonlinear systems with more manipulated inputs than controlled outputs is proposed. The technique is called habituating control as a result of its similarity to control schemes commonly used in biological systems. Nonlinear control laws that provide input-output linearization while simultaneously minimizing the cost of affecting control are derived. In the single-output case, the cost function employed differs according to the relative degrees of the two inputs. Local stability analysis shows that the resulting controller can provide a simple solution to the singularity and nonminimum phase problems. An extension of the controller design strategy for multiple-output processes also is presented. The proposed method is evaluated using nonlinear models of chemical and biochemical reaction systems.

Habituating control for nonsquare nonlinear processes

Nonlinear control of nonsquare multivariable systems

A controller design strategy for nonlinear systems with two manipulated inputs and one controlled output is proposed. The technique is called "habituating control" as a result of its similarity to control schemes commonly used in biological systems. A nonlinear control law that provides input-output linearization while simultaneously minimizing the "cost" of affecting control is derived. The cost function employed differs according to the relative degrees of the two inputs. Local stability analysis shows that the habituating controller can provide a simple solution to the singularity and nonminimum phase problems. The method is evaluated using a nonlinear chemical reactor model.

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Habituating control for non-square nonlinear processes

It is common wisdom that if a multivariable nonlinear system, affine in the controls, is non-minimum phase then dynamic inversion is not applicable for output tracking. We introduce a new approach in which a multivariable nonlinear control system is decomposed into two parts: a minimum phase part and a non-minimum phase part. For the minimum phase part dynamic inversion can be used to achieve output tracking. The non-minimum phase part can be suitably controlled by linear feedback, but the decomposition often leads to a simpler non-minimum phase problem than the original. It is necessary to restrict the class of output commands to be tracked according to the properties of the non-minimum phase part. These restrictions are identified by using results from robust control theory for commands that are perturbations of a command corresponding to a closed loop equilibrium.

A decomposition approach to output tracking for multivariable nonlinear non-minimum phase systems

This paper is concerned with the problem of designing a planar autopilot for the EMRAAT missile system using a modified variable structure control algorithm. A method is given for stabilizing the resulting nonminimum phase zero dynamics, and a tracking law using sliding modes is implemented in order to meet control objectives. The pitch autopilot employs a controller with time varying bandwidth in order to improve robustness.

Planar autopilot design for the EMRAAT missile using sliding modes

An asymptotic output tracking problem is studied for a class of nonlinear control systems with fewer outputs than inputs. The development is based on a standard relative degree assumption. The most interesting feature of the development is that the extra control degrees of freedom can be used to influence the closed loop characteristics, including the zero dynamics. Conditions are developed for when this approach is successful. >

D. Schumacher

Papers

An asymptotic output tracking problem for a nonlinear control system with fewer outputs than inputs