Piezoelectric ceramic hysteresis model linearization identification method based on Kalman operator
A piezoelectric ceramic and identification method technology, applied in neural learning methods, biological neural network models, design optimization/simulation, etc., can solve problems such as affecting positioning accuracy, achieve high positioning accuracy, avoid errors, and avoid complex derivation and approximation Effect
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specific Embodiment approach 1
[0023] Specific implementation mode 1: In this implementation mode, the piezoelectric ceramic hysteresis model linearization identification method based on the Koopman operator is implemented according to the following steps:
[0024] Step 1, establishing the hysteresis model structure of piezoelectric ceramics;
[0025] Step 2, determining the hysteresis model parameters of the piezoelectric ceramics;
[0026] Step 3, using simulation software to obtain a large amount of simulation data;
[0027] Step 4. Carry out deep learning training based on Koopman operator;
[0028] Step five, determining the linearization model of the piezoelectric ceramic hysteresis model based on the Koopman operator.
specific Embodiment approach 2
[0029] Embodiment 2: This embodiment differs from Embodiment 1 in that it is characterized in that the step 1 establishes the hysteresis model structure of the piezoelectric ceramic according to the following steps:
[0030] The hysteresis curve of the classic Preisach model can be divided into two parts: local hysteresis and global hysteresis. The Preisach hysteresis model is constructed by the superposition of multiple simple hysteresis operators. The superposition of a family of hysteresis operators with a given weight function can represent the global hysteresis, then the hysteresis model can be expressed as a series of weighted hysteresis operator superposition of:
[0031]
[0032] where x(t) represents the model output at time t, v(t) represents the model input at time t, and μ(σ,ε) respectively represent the basic hysteron operator and its weight function, which are usually called Preisach function.
[0033] The basic hysteresis operator is related to a pair of...
specific Embodiment approach 3
[0034] Specific embodiment three: the difference between this embodiment and specific embodiment one or two is that it is characterized in that the hysteresis model parameters of the piezoelectric ceramics are determined in step two according to the following steps:
[0035] Assume that the hysteresis operator in formula (1) The number of is limited, then the formula (1) can be expressed as:
[0036]
[0037] From the derivation of step one, it can be known that the displacement output of the piezoelectric ceramic driver can be determined as long as the value of the weight function is determined. First divide the rising and falling thresholds σ and ε into M equal parts respectively
[0038] σ i =ε j =(M-i) / (M-1)σ 1 , (3)
[0039] where σ 1 and ε 1 represent the positive and negative saturation input values of the piezoelectric ceramic actuator respectively, then the total number of hysteresis operators is M 2 .
[0040] First, obtain the function value table est...
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