High-Order High-Accuracy Unconditionally Stable Discretization Method

Discretization of continuous-time systems is an important and widely used technique to translate continuous-time models (CTM) to discrete-time models (DTM) needed to run it in digital computer architectures. Discretization techniques have been extensively studied and many methods have been proposed. The existing methods are subjected to constraints based on computer implementation efficiency, stability and accuracy.

Traditionally, the so called Integration Formulae (IF) such as Runge-Kutta and BDF (Backward Differentiation Formulae) are the most popular ones used in simulation, mostly because these methods are capable of high order approximation, and thus, they can provide high accuracy. Nevertheless, they achieve it at the expense of high computational cost and reduced stability what makes them inadequate to embedded system applications such as real-time filtering and control. The vast majority of embedded applications use the Backward Euler or the Trapezoidal Method. The first is unconditionally stable but is a first order method which implies reduced accuracy. The second one is a second order method but is marginally stable (not unconditionally stable).

Kylowave Inc. has developed a new discretization method which is unconditionally stable and can be easily tuned to achieve high-order without sacrificing its stability properties. In addition, our proprietary patent-pending method can be efficiently implemented in hardware or in software. The figure shows the comparison of Kylowave Inc. method compared to the most popular existing discretization methods for the case of a 5th-order filter. It becomes apparent from the figure that our method produces a significantly superior discrete-time approximation for the gain and the phase responses. The same result also applies for other digital filters and controllers. Please contact us to learn more how your applications can benefit from our technology.

High Accuracy Multi-Phase Permanent Magnet Motor Real-Time Model

Kylowave Inc. has developed a new high accuracy model for multi-phase permanent magnet motors such as BLDC (Brushless DC motor) and PMSM (Permanent Magnet Synchronous Motor) motors. Based on our patent pending technology, we are currently implementing an HDL a real-time high speed and high accuracy model for multi-phase BLDCMs and PMSMs motors.

These models are useful in test and verification of intelligent motion controllers for advanced mission critical applications such as Underwater Unmanned Vehicles (UUVs) and Unmanned Aerial Vehicles (UVs). Other applications required to comply with demanding safety standards would also significantly benefit from our technology.

FPGA-Based Hardware Acceleration of Complex Algorithms

Traditionally, simulation and control applications requiring higher speed and higher accuracy have relied on the advancements made to the microcontrollers and DSPs in order to achieve higher performance. Despite the remarkable progress made on those technologies during the last three decades, it has been recently reported their pace of progress started to slow down as those technologies achieved maturity. For example, ten years ago the minimum simulation time step for a commercial state-of-the-art cluster-based real-time simulator was around 20 microseconds. Nowadays, ten years later, it is at best at 5 microseconds if we exploit every resource the present technology can offer.

Trends reported by mainstream automotive suppliers have already indicated the potential advantages of FPGA devices compared to the microcontroller and DSP technologies. Their capacity to implement and integrate both software and digital hardware functionalities on a single component is very attractive to reduce complexity and increase integration. Despite it, one main challenge preventing its widespread adoption, however, may be one of design methodologies encompassing design, implementation, simulation and verification of the product.

Kylowave Inc. has developed a proprietary technology to map complex multi-physics algorithms into massively parallel processing architectures such as FPGAs. Our technology allow us to map the algorithms directly in a hardware description language such as VHDL, thus, avoiding the speed limitations created by the separate memory-processor paradigm adopted by microcontrollers and DSPs. Combined with our proprietary patent-pending discretization, we can map linear and nonlinear dynamical models (controllers, filters, motor models, etc.) automatically into a reconfigurable hardware such as FPGAs. The experimental results shows that this approach achieves a speed up of more than one order of magnitude compared to the existing technologies. Similar speed up has been obtained with real-time simulation and control applications.