## 1 Introduction
The main ideas of the dynamic programming approach exposed here were originally proposed in ref. [19]. This approach was applied to the unmanned aerial vehicle (UAV) in ref. [20], an autonomous soaring UAV in ref. [21], to a hybrid exoskeleton in ref. [22], and a tomato debbrator modeled as discrete affine nonlinear systems with delayed input [23]. Since the rotor flux is not usually measurable, in some cases, it is obtained via an observer. However, in this proposal, the real-time reconstruction of the fluxes is carried out according to ref. [24]; that is, using measured variables and the mathematical model. These flux estimations, the stator currents (obtained from an industrial VFD Delta VFD007 EL11A), and the rotor speed (measured from an encoder) are used for the computation of the proposed nonlinear discrete suboptimal control, which uses the plant model. The real-time experiments are made using a data acquisition NI MyRIO card, an industrial VFD, and LabVIEW software, in which a command interface is developed to set the setpoints (experimentally obtained), the penalty matrices for computation of the discrete suboptimal controller, and the nonlinear control strategy. The inner PID control of an industrial VFD, usually used to regulate the velocity of the rotor of the motor, is tuned (the proportional part is the unity, the integral and derivative parts are disabled) to allow the external control signal from the MyRIO card and the PC with LabVIEW software. The setpoint of the inner PID of the VFD is set to zero using the potentiometer available from the VFD. The internal PID control of the VFD is configured with positive feedback (the part of the process variable is positive and configured as an analog input of the VFD). In this analog input, the suboptimal nonlinear control signal, given by the MyRIO card (a root mean square voltage that is proportional to frequency, which guarantees the relation of V/F of the VFD) is introduced to the industrial VFD instead of the encoder signal. The encoder signal is read through the MyRIO card and processed using LabVIEW software. A comparison with an optimal PI controller using the VI LabVIEW PID of the Control toolkit is made. The main contributions of the paper are summarized as follows:  
* The experimental application of the discrete suboptimal controller for the nonlinear induction motor model is developed with a relatively low cost to regulate the five state variables of the biphasic system. * An industrial VFD is used as interface between the nonlinear control and the AC motor by using a MyRIO card and LabVIEW software. The experiments were conducted with different sampling times. * The real-time reconstruction of the rotor fluxes is obtained directly from the nonlinear model and is used to calculate the suboptimal nonlinear discrete control. * Good tracking performance and robustness to unknown parameters is obtained when the set point is varying (without and with load on the motor shaft). The proposed suboptimal nonlinear discrete controller improves the operation of the V/F scalar control (currents and fluxes tracking) of the industrial VFD when compared with an optimal PI. It gives experimental evidence that the mathematical model used is a good approximation of the real behavior of the AC motor. This paper is organized as follows. Section 2 is devoted to useful results for the implementation of the proposed scheme. In Section 3, the suboptimal sequence to regulate a transformed biphasic system is synthesized. The experimental results are presented in Section 4, and finally, in Section 5, concluding comments are presented.