A mechanical plant is described by a linear difference equation yk+ayk-1+azyk-2-boux. In order to identify the plant parameters, a signal generator is used to generate signal u to excite the plant. At the same time, a sensor is used to collect the plant output signal y. The following segments of signals are collected: {v}={86.5747, 125.5091, 148.2536, 155.3899, 145.8313, 122.0516, 85.7713) {u}={ 1.5374, 0.1401, -1.8628, -0.4542, -0.6521, 0.1033, -0.2206} (a) Use the available data to identify the plant parameters. (30 marks) (b) Obtain the controllable canonical form for this system. (10 marks) (c) Obtain the observable canonical form for this system. (10 marks)