# Questions tagged [control-theory]

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### Animation of system response with python [closed]

I am trying to animate the root locus for a tranfer function G as kp, changes. This is my code: ...
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### Determine the transfer function of a movement equation

The problem is the following. I have to control a spaceship (assuming no gravity, no mass, no friction / no external forces). In other words, the first equation in this question leads to $0 = 0$. My ...
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### Lyapunon candidate function to derive parameters estimation law

I have a system and a reference model represented in state space in the following form: \begin{gather} \dot{x} = Ax+Bu \\\ u = \hat{K}(t)x+\hat{k}_r(t)r \\\ \\ A_m = A+BK \\\ Bk_r = B_m \\\ K,k_r : \...
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### What does “Coupling Effect” refer to in MIMO systems?

Here is the block diagram of the system. G11 relates the input R1 to the output Y1, G12 relates the input R1 to the output Y2 similarly for R2. What is the effect of coupling-which is as I know is ...
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### Input-output representation to state space

How do you create a state space representation of the following input/output equation: $$\dot{y} = -ky + u + a\sin(ωt)$$ where the parameters $k$, $a$, and $ω$ are unknown. The end goal is to ...
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### Root Locus and Routh–Hurwitz stability criterion

A satellite launcher has a unit feedback system, whose TF global open loop is given by: $$G_c(s)G(s) = \frac{K(s^2-4s+18)(s+2)}{(s^2-2)(s+12)}$$ a) Draw the root locus for this function b) ...
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### avoidance with LQR

I'm interested in using linear quadratic regulators (LQR) to model prey avoidance behaviors. I want to adapt the LQR algorithm to incorporate dynamics and state costs that maximize the distance from a ...
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### How to obtain transfer function of control diagram with Internal Model Control?

I want to design a robust control system using the internal model design specifications. The block diagram is the one shown below: I am trying to obtain the transfer function $\ \frac{Y(s)}{R(s)}$ ...
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### Tuning a cascaded attitude and attitude rate PID controller

Assume that I have an object in 3D, and I want to have a controller that stabilizes its orientation (also referred to as "attitude"). To be sure we are clear: attitude is measured in "degrees" or "...
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### Applying full state feedback on DC motor with torque load

I tried to apply full state feedback on DC motor (with no load) and it works fine in the simulation on Simulink But the question is if I have a load applied on the motor (let’s say constant load or ...
Consider we have a second order system (plant) described by the following transfer function: $$P(s) = \frac{b_0}{s^2+a_1*s+a_2}$$ which is controller by a PD-controller: $$C(s) = K_p+K_ds$$ ...
I have a real mechanical system (ball & beam) which I want to control. The system is approximated by the second order transfer function: $$T(s) = \frac{b_0}{s^2+a_1s+a_2}$$ and in state-space ...