An adaptive, discrete-time sliding mode controller (SMC) is disclosed which detects and adapts to gain variations in the controlled plant. The overall control effort is generated by combining a linear control effort with a discrete-time sliding mode control effort generated by switching between gains in order to drive the system's phase states toward a sliding line trajectory. A sliding mode variable &sgr;k defines the position of the system phase states relative to the sliding line. The SMC controller is designed such that the sliding mode variable &sgr;k crosses the sliding line and changes sign at every sample interval. For the nominal plant gain, the SMC controller is also designed such that the magnitude of the sliding mode variable &sgr;k+1=−&sgr;k will remain constant (&sgr;k+1=−&sgr;k) and substantially constrained to; ;where &Dgr; and &lgr; are predetermined design constants. The deviation in if the magnitude of &sgr;k from nominal is a direct measure of the deviation in the plant gain. Accordingly, the present invention measures the error between the measured magnitude of &sgr;k and the nominal magnitude, and uses this measured error to adapt to variations in the plant gain.
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机译：公开了一种自适应离散时间滑模控制器（SMC），该控制器检测并适应受控工厂中的增益变化。通过将线性控制功与通过在增益之间切换而产生的离散时间滑模控制功相结合来产生总体控制功，以将系统的相位状态驱动到滑线轨迹。滑动模式变量＆sgr; k 定义系统相位状态相对于滑动线的位置。 SMC控制器的设计使得滑动模式变量＆sgr; k 越过滑动线，并在每个采样间隔更改符号。对于标称植物增益，还对SMC控制器进行了设计，以使滑模变量＆sgr; k＆plus; 1 ＆equals;＆minus;＆sgr; k 的大小保持恒定。 （＆sgr; k＆plus; 1 ＆equals;＆minus;＆sgr; k ）并基本上限于： <数学> <！[CDATA [＆verbar;＆sgr; k ＆verbar;＆equals ;＆Dgr //（ 1 ＆lgr;） ]]> ;其中＆Dgr;和＆lgr;是预定的设计常数。 ＆sgr; k 的大小与标称值之间的偏差是对植物增益偏差的直接度量。因此，本发明测量了测量的＆ k＆ k 的幅度与标称幅度之间的误差，并使用该测量的误差来适应植物增益的变化。
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