# Questions tagged [control-systems]

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### A good textbook for designing signal filters

Since a couple of months ago I started being actively involved in the area of control of dynamical systems. In most cases, designing a controller for a given dynamic system will require the ...
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### Digital control: Exercise solution

Can you help me (show me how) to solve the following exercise? For the process with transfer function $G(s)=e^{-2s}/(s+1)$ design a digital controller with sampling time $T_{s} = 1$ that meets the ...
2answers
485 views

### Control design: under what conditions can closed-loop poles be placed arbitrarily?

Say we have a single-input linear system $\dot{\mathbf{x}} = A\mathbf{x}+Bu$. With full-state feedback ($u=-G\mathbf{x}$), it is straightforward to arbitrarily place the $n$ closed-loop poles (i.e., ...
1answer
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### SRF-PLL discretization problem

So I've been working on how to digitally implement a static reference frame PLL (SRF-PLL), which is a quite popular PLL used for extracting three-phase grid angle. This PLL works by using the DQ0 ...
1answer
662 views

### Determining the final value of the output of a discrete system

I'm going through an exam question where I've been told that the samples $f(kT)$ of the following function \begin{equation}{F\left(z\right)=\frac{1}{1-0.819z^{-1}}} \end{equation} are applied to a ...
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### Find transfer function from root locus and step response diagram?

I am given the response of a step of magnitude of 3 and the root locus and I have to find the transfer function of the system. The function I find gives me the step response(magnitude of 3 again) of ...
1answer
519 views

### Benefits of oversampling in a realtime noise-cancellation system

When sampling a signal, it is standard practice to use a sampling rate that is greater than two times the bandwidth of the signal in order to avoid aliasing. The result is then low-pass filtered (and ...
2answers
556 views

### How to intuitively understand the state space formulation of discrete time system?

The SS formulation of DT system is given by $$x[(k+1)T] = Ax(kT) + Bu(kT)$$ $$y(kT) = Cx(kT) + Du(kT)$$ Note: T is the sampling period and often omited Can someone explain to me why the state ...
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160 views

### How to periodically estimate states of a LTI if the output is measured irregularly?

How can I periodically estimate the states of a discrete linear time-invariant system in the form $$\dot{\vec{x}}=\textbf{A}\vec{x}+\textbf{B}\vec{u}$$ $$\vec{y}=\textbf{C}\vec{x}+\textbf{D}\vec{u}$$...
0answers
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### How do I check controllability and observability using Gramian matrixes?

I have a pending exam and this is one of the must-know questions. It will be about checking controllability/observability of a simple MIMO linear system, using Controlability Gramian/Observability ...
0answers
105 views

### Optimal inference for nonlinear state space models

When considering a linear-Gaussian state space model, it is often referred that, optimal inference is tractable which is very rare in state space models. When considering a nonlinear state space model,...
1answer
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### survey/book on adaptive/self-tuning of PI controllers?

Can someone point me towards a good book or survey article on adaptive/self-tuning of PI controllers? All I can find online are articles which are either vague or heavy on theory.
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### What is the Reference in Control Theory?

I've started studying Control and I've come across some concepts that I'm finding a bit difficult to understand. For example, in the system showed here, there is a signal called "reference" as well ...
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### Exponential decaying step response in LTI System

I'm attempting to better understand the relationship between step responses, impulse responses, and convolutions. Say that I have a system where if I apply a constant input, my output decays from a ...
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### What is the difference between a lag filter and “PI” control?

A lag filter/compensator has the form $$G_c(s) = \frac{s+z}{s+p}$$ with $-z < -p < 0$. In practice, the effect of lag compensation in feedback control is to increase the DC gain of the open-...
3answers
433 views

### Do FIR filter have any application in control theory?

I know about IIR filter as discrete pendent to transfer functions in the Laplace domain. So it is actually quite simple to convert the function of the control system and finally receive the discrete ...
2answers
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### Kalman filter with accelerometer with DC offset

Goal: For a particle moving uniaxially, to estimate position ($d$) and velocity ($v$) from noisy acceleration ($a$) and very noisy position (GPS) measurements using a Kalman filter. Catch: The ...
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57 views

### Controllable realisation of $\frac{s^4+1}{4s^4+2s^3+2s+1}$ is both controllable and observable?

I am trying to find the controllable realization of the following transfer function: $$H(s)=\frac{s^4+1}{4s^4+2s^3+2s+1}$$ I approach this by first using polynomial division to assure that $H(s)$ is ...
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103 views

### Time invariance of a System

I have this small question about the time invariance of a system. Which is: If the current output is multiplied by the current input (see both are variables) will the system be time variant or time ...
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### Control theory: how do you initialize input for a model predictive controller?

Although I think this is a pretty popular algorithm, I posted this question on electronics stacksexchange but received no response. I am posting it here to see if there are many signal/control experts ...
1answer
383 views

### How to do this root locus by hand?

I have an open-loop system function $$L(s)=6\frac{(s-2)^2}{s(s-20)^2}$$ and I wanted to to the root locus diagram for it. I did it in MATLAB and got the following graph What I don't know how to do ...
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293 views

### Why is it necessary to have two state variables

I am learning about control theory. Let's consider this system. $$m a(t) + b v(t) + k x(t) = f(t)$$ $a$ is acceleration $v$ is velocity $x$ is displacement $f$ is external force In my ...
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### For a standard second order transfer function, what is the equivalent time domain significance of $\zeta>0.707$?

In frequency domain $\zeta>0.707$ implies no resonant peak in frequency response. But I am unable to correlate what is the exact time domain effect of this? If $\zeta=0.707$ acts like an '...
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### Transient response of system with single pole $0 \le p < 1$

$G(z) = \frac{1-p}{z-p}$ If the value of p satisfies $0 \leq p < 1$ there are no oscillations in the transient response. Question: Why is that $\uparrow$ true? I know roughly what a ...
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49 views

### Books on delay / lag compensation

Which books do you recommend that provide comprehensive overview of delay compensation techniques in control systems?
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### Control systems and convolution

I think i am not understanding the concept of convolution well. Lets say we are given a system impulse response in the S-domain, and we have implemented a controller $G_c(s)$ that will adjust the ...
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### State Space Observer Control

I am attempting to implement observer based state feedback in C and can't figure it out. Here is pseudocode of the algorithm: ...
1answer
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### response of algorithm in non-equidistant time

We are investigating ways to test a control algorithm. The algorithm has a non-equidistant track of input data (i.e. not every sample is valid, and we know it), and should output a series of ...
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### General tips for PID tuning of super low-friction actuator?

I realize this question is not directly related to signal processing, however, it's relevant to system analysis which is relevant to most signal processing engineers. There's also no good alternative ...
1answer
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### Orthogonal signal generator using integer arithmetic

I have a problem with implementing an orthogonal signal generator (OSG) algorithm on a microcontroller using integer arithmetic. I use this algorithm for a single-phase phase-locked loop (PLL) ...
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### What are the advantages of LTI ( Linear Time Invariant ) systems over other systems? [duplicate]

In our engineering academics, there is one subject named "signals and systems". In this subject only LTI system is discussed. I want to know what are the advantages of LTI systems over other ...
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### State space equations

I am stuck on this exercise. I don't know how to deal with this squared y in the denominator. What am I supposed to do to obtain state space equations? ex.1 Simplified dynamic model of the steel ball ...
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### In the context of transfer functions, what is the relationship between the terms “proper”, “causal”, and “realizable”?

I am thinking about these terms in the context of linear control. A transfer function is proper if the degree of the numerator is not greater than the degree of the denominator. I've read often that ...