Chapter 1
Control systems, Linear systems, transfer functions, state space related problems

 1.1 Creating tf and state space and different Conversion of forms
 1.2 Obtain the step response of an LTI from its transfer function
 1.3 plot the impulse and step responses of a system from its transfer function
 1.4 Obtain the response of a transfer function for an arbitrary input
 1.5 Obtain the poles and zeros of a transfer function
 1.6 Generate Bode plot of a transfer function
 1.7 How to check that state space system \(x'=Ax+Bu\) is controllable?
 1.8 Obtain partial-fraction expansion
 1.9 Obtain Laplace transform for a piecewise functions
 1.10 Obtain Inverse Laplace transform of a transfer function
 1.11 Display the response to a unit step of an under, critically, and over damped system
 1.12 View steady state error of 2nd order LTI system with changing undamped natural frequency
 1.13 Show the use of the inverse Z transform
 1.14 Find the Z transform of sequence x(n)
 1.15 Sample a continuous time system
 1.16 Find closed loop transfer function from the open loop transfer function for a unity feedback
 1.17 Compute the Jordan canonical/normal form of a matrix A
 1.18 Solve the continuous-time algebraic Riccati equation
 1.19 Solve the discrete-time algebraic Riccati equation
 1.20 Display impulse response of H(z) and the impulse response of its continuous time approximation H(s)
 1.21 Find the system type given an open loop transfer function
 1.22 Find the eigenvalues and eigenvectors of a matrix
 1.23 Find the characteristic polynomial of a matrix
 1.24 Verify the Cayley-Hamilton theorem that every matrix is zero of its characteristic polynomial
 1.25 How to check for stability of system represented as a transfer function and state space
 1.26 Check continuous system stability in the Lyapunov sense
 1.27 Given a closed loop block diagram, generate the closed loop Z transform and check its stability
 1.28 Determine the state response of a system to only initial conditions in state space
 1.29 Determine the response of a system to only initial conditions in state space
 1.30 Determine the response of a system to step input with nonzero initial conditions
 1.31 Draw the root locus from the open loop transfer function
 1.32 Find \(e^{A t}\) where \(A\) is a matrix
 1.33 Draw root locus for a discrete system
 1.34 Plot the response of the inverted pendulum problem using state space
 1.35 How to build and connect a closed loop control systems and show the response?
 1.36 Compare the effect on the step response of a standard second order system as \(\zeta \) changes
 1.37 Plot the dynamic response factor \(R_{d}\) of a system as a function of \(r=\frac{\omega }{\omega _{n}}\) for different damping ratios
 1.38 How to find closed loop step response to a plant with a PID controller?
 1.39 How to make Nyquist plot?