Reference no: EM13371422

A two control inputs - two controlled outputs plant is described by the state - space model:

                    state equactions       (1)

                               controlled output (2)

where  are the states, controlled outputs, control inputs and disturbance input, respectively.

The plant states and disturbance input are NOT measurable while noise free measurements of the controlled outputs are available. The disturbance input is unknown.

(I). Design an integral controller so that  for any piecewise constant reference vector of the controlled output vector in spite of the piecewise constant disturbance input.

• The location of poles in the closed loop is not prescribed. Define the piecewise constant scenarios of and z(t) and find the desired poles for the state feedback controller and state observer by a method of trial and error based on general knowledge of the poles impact on the transient processes so that the transients during the reference output tracking meet your high requirements in time domain.

• During the control system design process calculate the appropriate gains using PLACE subroutine of Matlab.
• Validate the control system tracking performance by simulation performed for the selected the following scenarios of z(t) and: constant, piecewise constant, ramp, sine wave with varying rate of change. Discuss the results and point out on the controller limitations with regard to the rate of change of the system inputs.

(II). Improve the controller designed in part (I) by introducing a mechanism for the disturbance compensation at the plant input. Illustrate advantage of the improved controller by applying the fast varying piecewise constant reference input vector and sinusoidal disturbance.