1.

The observer-controller developed in the Chapter 7 self-test is shown below. The states are x = [ ? x ] ^T, the output is y = F, and the inputs are u = [ ? x F] ^T. Create a continuous-time state-space MATLAB model of this system.

2.

Discretize the continuous-time model of problem 1 with a step time of 10 milliseconds and a first-order hold approximation.

3.

Plot the unit step response and frequency response from input 1 (0) to the output ( F) of the discrete-time observer-controller and compare them to the responses of the continuous-time observer-controller.

4.

Implement the observer-controller in C++ with floating-point mathematics. Use write_cpp_model() for this.

5.

Use the scaling vectors u _s = [4 2 1000], x _s = [2 1 100 20], and y _s = [1000], to implement the observer-controller in C++ with fixed-point mathematics. Use write_cpp_fixpt_model() for this.

6.

Write a C++ program that iterates the floating-point and fixed-point models created in the previous two problems for 10 time steps (0.1 seconds) and stores the results in a text file that can be read by MATLAB. Use [1 0 0] ^T as the system input vector and set the initial states to zero.

7.

Plot the outputs of the fixed-point and floating-point models from the previous exercise along with the response of the continuous-time model in MATLAB.

8.