Transition to Digital: Number Crunching

A Digital Signal Controller (DSC) is a single-chip, embedded controller that seamlessly integrates the control attributes of a Microcontroller (MCU) with the computational and throughput capabilities of a Digital Signal Processor (DSP) in a single core.

The dsPIC® DSC balances its outstanding MCU qualities with real DSP performance using numbers to represent physical values.

• Advantages: The system can directly operate on the equations that describe the system functionality. This allows power conversion designers to use different control techniques, topologies, and modes without the need to change anything on the board, i.e. increased flexibility.
• Disadvantages: Care must be taken in using numbers because precision is not infinite (in loop controllers, fixed point mathematics is used). The consequence of this is that overflow may be generated. Secondly, a finite interval of time is required for the unit to compute the output although it's also true that the output is generated with delay in the analog domain within the loop, e.g., from the compensator.

There are a number of different approaches that can be used to design the digital equivalent of the analog compensator (controller).

In the digital domain, it is possible to implement control techniques that is not possible to implement in the analog domain. For example:

• Direct transformation of the analog compensator transfer function to the digital version
• Proportional, Integral, Derivative (PID) approach
• State variable approach
• Direct digital synthesis
• Non-linear controllers

The next section focuses on using Proportional, Integral, and Derivative (PID) controller to describe how dsPIC® DSC number crunching can be used in power conversion applications.

#### Proportional, Integral, and derivative (PID)

The Proportional, Integral, and derivative (PID) controller is commonly used in the control loops of industrial processes. Its parameters need to be adjusted as a function of the control process and remain unchanged during normal operations. See figure below.

The following is the PID equation, where e(t) is the error of the system; Ts is the signal sampling period (instantaneous time) and Kp, Ki and Kd are the proportional, integral and derivative controller gains.

The above demonstrates that PID requires numerous calculations and constant parameter adjustments during operation. The dsPIC® DSC's DSP engine allows fast math operations with the following features:

• High-speed 17-bit by 17-bit multiplier
• Barrel shifter