Notation	Explanation
$\mathsf{\delta }{\Delta }_{out}$	Positioning error of the micro-positioner
${\mathsf{\epsilon }}_p$	Positioning error of the driving stage
${\mathsf{\epsilon }}_s$	Positioning error of the machining stage
${\mathsf{\epsilon }}_c$	Positioning error of the measuring stage
$w\left(=x,y,z,\alpha ,\beta ,\gamma \right)$	6-DOF of the micro-positioner
$v(=b,m,t)$	Top, middle and bottom platform of the compliant mechanism
$f_w$	Implicit functions of motion
$w_{out}$	Output displacement of micro-positioner
$w_{pzt}$	Load output displacement of PZTs
$w_{pzt0}$	No-load output displacement of PZTs
$\delta w_{pzt}$	Driving error of PZTs
$\delta w_{cp}$	Measuring error of the micro-positioner
$\delta w_{out}$	Positioning error of the micro-positioner
$\delta d_{wi}$	Machining error of the geometric parameters
$\varsigma$	Ideal linear ratio of the output displacement to the input voltage of PZTs
$H\left(u_{pzt}^w\right)$	Hysteresis nonlinear model of PZTs
$p_{pzt}^w\left(\right)$	Preisach function
$\mu \left(\right)$	Weighting function
${\widehat{\gamma }}_{\alpha \beta }$	Hysteresis operator
$\widehat{\alpha }$ , $\widehat{\beta }$	Up and down switching value of the input voltage
$u_{pzt}^w$	Input voltage of PZTs
$u_{in}^w$	External voltage supply of PZT controller
$m_w$	Equivalent mass of compliant mechanism
$c$	Equivalent damping coefficient of compliant mechanism
$k_w$	Equivalent stiffness of compliant mechanism
$k_{in}^v$	Input stiffness of compliant mechanism
$k_{pzt}$	Stiffness of PZT
$F_{pzt}^w$	Driving force of PZTs
$q$	Electric charge of PZTs
$F_{in}^w$	Input driving force of compliant mechanism
$n$	Number of piezoelectric ceramics of PZTs
$h_c$	Amplification ratio of PZT controller
$R_c$	Equivalent resistance of PZT controller
$C_c$	Equivalent capacitance of PZT controller
$G_{pzt}^w\left(s\right)$	Transfer function of PZT
$G_{stage}^w\left(s\right)$	Transfer function of the stage
$G_w\left(s\right)$	Transfer function of the entire system
$w_{\mathrm{pzt}}^{\mathrm{d}}$	Expected output displacement
$\lambda$	Displacement amplification ratio of the compliant mechanism
$w_{pzt}^p$	Load output displacement of PZTs of PID controller
$t$	Time variable
$K_p$	Proportional gain of PID controller
$T_i$	Integral time of PID controller
$T_d$	Derivative time of PID controller
$\mathsf{\theta }$	Input matrix of BP-PID controller
$f\left(\mathsf{\theta }\right)$	Output matrix of BP-PID controller
$W^{(1)}$	Weight matrix of the hidden layer
$W^{(2)}$	Weight matrix of the output layer
${\mathsf{\rho }}^{(1)}$	Threshold matrix of the hidden layer
${\mathsf{\rho }}^{(2)}$	Threshold matrix of the output layer
$\phi \left(w\right)$	Activation functions of the hidden layer
$g\left(w\right)$	Activation functions of the output layer
$a_i$	Binary selection vector of CMAC neural network
$w_{pzt}^n$	Load output displacement of PZTs of CMAC neural network
$\chi$	Generalization parameter of CMAC neural network
$E$	Performance indicator function
$e_{loop}$	The maximum hysteresis error
$e_{\mathit{max}}$	The maximum positioning error
$e_{rms}$	The root-mean-square error