Mathematical programming methods applied to design of computationally optimized digital controllers

The design and implementation of a class of computationally optimized digital controllers is proposed. It is assumed that multiplications are the most complex part of the implementation. To reduce the computational complexity of the controller, its coefficients are expanded to the power of two and the controller equation is formulated in the form of a sequence of shift and addition/subtraction operations. Therefore, the multiplications are cancelled and a computationally more efficient formulation is obtained. A nonlinear programming algorithm is then developed to choose the controller coefficients so that the number of shift and add/sub operations is minimized. Both time and frequency domain designs are considered