A new hybrid method for the order reduction of a high-order, linear, time-invariant disk drive read system is proposed. The method generates a lower-order stable model, retaining both the initial Markov parameters and time moment of the original system. The method is simple, direct and computationally superior compared to other methods. The reduced-order model transfer function of a disk drive read system is derived using the proposed method. The responses of the original system and the second-order reduced system for unit step and unit impulse inputs are evaluated for amplifier gain value of K_a = 10. It is observed that the transient response of the second-order system obtained by the proposed method is significantly improved.

A hybrid method is proposed for finding a stable reduced-order model of a disk drive read system using the Pade approximation technique and the Routh-Hurwitz array. This method guarantees stability of the reduced model when the original system is stable. Reduced-order models are often required in the analysis and synthesis of high-order complex systems to reduce computational time and memory requirements and also for online applications (Chen and Shieh, 1968). Various techniques like the Pade approximation technique and Routh approximation technique have been successfully used to find reduced-order representations of high-order systems (Chuang, 1970; Chuang, 1976; Gutman et al., 1982; Lepschy and Viaro, 1983; Pal, 1983; Sastry and Krishna Murthy, 1987; Lucas, 1988a; Lucas, 1988b; and Lucas, 1992). This method has the disadvantage that the reduced model may be unstable although the original system is stable. Several methods (Shamash, 1974 and 1975) are available for arriving at stable reduced-order Pade approximants. Shamash (1974) used the Koenig's theorem to compute the smallest (or the largest) magnitude pole of the original system that must be retained in the reduced-order model.

This method suffers from the drawback that once the resultant model is found to be unstable, a successively higher number of original system poles are retained and the reduced-order model is checked for stability each time. In the method explained in Shamash (1975), the appropriate number of dominant poles is retained. This requires determination of the poles of the system, which may lead to computational problems for very high-order systems or when the system has closely spaced repeated poles. Chuang (1976) has proposed a `partial solution' to the stability problem, through the homographic transformation s = w/(a + bw), which gives a family of reduced models of the same order. This method involves more computation and has the further shortcoming that the choice of a and b is arbitrary. If an unstable model results for a particular choice of a and b, one has to resort to the trial-and-error procedure of trying out other combinations.

The denominator polynomials D_k(s) (k = 1, 2, , n) of the reduced-order models are obtained by a Routh-type array. The Routh Array is constructed as shown in Table 1. The elements in rows 3 downwards are calculated as follows: The row in each case is formed from elements in the two rows above the element being calculated using the value in column 1(pivot column) and the value in the column to the right of the element being calculated. The denominator is the element in the pivot column in the row above the element being calculated. The calculated element is set to 0 if the row is too short to complete the calculation.

Electrical and Electronics Engineering Journal, Disk Drive Read System, Pade Approximation Techniques, Homographic Transformations, Routh Array, Routh Approximation Techniques, Notebook Computer, MATLAB Program, Markov Parameters, Model Reduction, Modern Control Systems.