Questions tagged [control-theory]
The control-theory tag has no usage guidance.
414
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Control techniques for linearized systems (I.E. a linearized DC-DC boost converter)
I have a linearized model of a DC-DC boost converter, in matrix form:
$x' = Ax + bu + d$
(the two "x" states are the input inductor current, and the output capacitor voltage)
For controlling ...
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How and why is kinematic control implemented?
First off, I apologize for what is likely a rather broad and formless question (and an even more broad and formless title). I'm a mathematician whose work sometimes carries him to control systems due ...
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Why is it true that the velocity error constant can be read from the Bode diagram at the frequency w=1 rad/s?
I am trying to find a proof as to why we can read the velocity error constant $K_v$ of a closed-loop directly from the Bode diagram. That is, why the following is true: $K_v = \frac{|L(j\omega)|}{\...
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I need to design a controller for a system, need to choose between P, PI, PD, and PID, given only the desired ss, settling, and overshoot %
(Apologies for terrible formatting, first post and don't know how to make equations look nice)
The system is
$$G(s)=\frac{10}{4s^2+7s+23}$$
and the requirements are steady state error of zero, $10ms$ ...
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How does frequency-response and lead-lag compensators fit in with PID or State Space control
I am new to control theory, as my background is in statistics. In watching a wonderful set of lectures by John Rossiter, and am feeling pretty comfortable with my understanding of the basic concepts ...
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Calculating residual in a system based on parity space approach
I am reading the book Model-Based Fault Diagnosis Techniques, where the chapter on Residual Generation Methods has a section on the Parity Space Approach.
Here, it is said that residual $r(k)=(y_s(k) −...
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Output error vs equation error
We are learning about the parity space approach in class and we were given this figure to demonstrate the output error and equation error. [![Output and equation error][1]][1]
My question is what are ...
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Creating a recursive control system
I am trying to design a digital control system of which output depends on the difference between 1 input signal 1 tick ago and the output 1 tick ago ,and 1 another input signal.
The output $y(n)$ = ...
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Partial derivative of change in state with respect to multiplicative faults
I am reading the book "Model-Based Fault Diagnosis Techniques" by Steven X. Ding. Here, they describe a system with the equation $$ ẋ = (A + ΔA_F)x +(B + ΔB_F)u+E_f f$$ Then, $$ ΔA_F = ...
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What is the physical intuition behind an "integrator" in control theory
I am watching some videos on control theory by John Rossiter, and they are very good. So far I have watched most of the videos on classical control, including transfer function, feedback, etc.
One ...
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State space representation of a 2 tank system
I am figuring out the state space equations of a connected 2-tank system. For the 1st tank, the state space equation is as follows :
...
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Final form of transfer function in a single input single output system
I am reading the textbook "Modern Control Engineering" by Katsuhiko Ogata. There is a section on deriving the transfer function from the state space equations dx/dt = Ax + Bu and
y = Cx + Du
...
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197
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Transfer functions of a closed loop system subjected to a disturbance
There is a system with two controllers in series having the transfer functions G1(s) and G2(s) which is separated by a summing point through which the disturbance D(s) enters the system. The output ...
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Model mismatch and bias in Smith Predictors
I have a question pertaining to Smith Predictors (see below for reference). Given a plant P and plant model Gp, I believe model mismatch is irrelevant in steady state. In steady state, delay-less ...
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Obtaining the open loop gain - (estiamte the gain and phase frequency response)
This post is related to the following stackexchange link but in this new question, I am focusing on describing the controller and going over my process of obtaining the open loop vs closed loop gain: ...
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controls - how to measure phase margin for low gain system
I have a closed loop system with the corresponding gain and phase plots shown below (note frequency is normalized). I am interested in identifying the phase margin and gain margin of my system.
In ...
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Some questions about model predictive control (MPC)
I have some questions about model predictive control (MPC)
How does MPC use a system's model to forecast its future response?
How do model uncertainties and mismatches affect the performance of MPC, ...
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How do you linearize this nonlinear system?
The system equations are:
$$
\ddot{\theta} = -\alpha \; |\theta| \; \theta + \sin(\theta) - \tau
$$
$$
\tau(t) = 20 \; e^{-20t} \; v(t)
$$
The system state space description is:
$$
\mathbf{x} = \begin{...
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How to implement H-infinity controller in STM32 platform?
I used matlab to simulate some H infinity controllers, and I have some understanding of the related theory. But I don't know how to implement H-infinite controller on STM32 platform using C/C++ code.
...
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Entire Complex Function for dynamical systems
I am working on my master Thesis and I was going through this Thesis : https://scholarship.rice.edu/bitstream/handle/1911/89289/RICE0327.pdf?sequence=1&isAllowed=y
Here, the author computes the ...
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What is the Z transform of the Discreate PI control model？
I have a discreate PI controller implemented in stm32 MCU, it has the following form:
$$
PI=K_p\cdot[r(t_i)-y(t_i)] + (K_I)\cdot\sum_{n=0}^{i}[r(t_n)-y(t_n)]\cdot\Delta t
$$
where
$r(t_i)$ is the ...
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Multiloop feedback control system find closed loop gain
I want to find the closed loop gain of this block diagram:
I remember a rule that since these 2 loops collide with each other we ignore them so is the closed loop gain just equal to $\frac{H_{1}(s)}{...
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Routh's algorithm and root analysis give contradictory results
I am designing a control system :
with open loop gain equal to : $\frac{K}{s(s^{2}+4s+3)}$
The closed loop gain is obviously :$\frac{K}{s(s^{2}+4s+3)+K}$
I tried finding the critical frequency but ...
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2
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49
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Different kinds of control loops
I am wondering about different categorizations of control loops. One categorization differentiates control loops with respect to what inputs they take:
Open control loops.
Closed control loops.
1a. ...
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Error Equation of a Control Loop
I want to calculate the error of a control loop. Therefore, the system and the general processes and models are defined as follows:
The equation for error is described as follows:
I do not ...
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What is the intuitive explanation for why a system can be stable with a negative gain margin?
Beyond the math which shows that a gain of -1 and a phase of -180 (G(s)=-1)causes instability when the open-loop TF is taken to closed loop, the way I've always justified the instability of G(s)=-1 ...
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How to re-write systems of two linear second order ODEs in a state space form
I have recently been working on how to convert ODES into state space form, and I came across this problem that has me confused. Should B in the state space be [1; -2] or [1 0; 0 -2]?
I think the ...
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How often is discrete-time control used in industry?
Although in reality I know that computers handle all systems in discrete time, in my limited industry work experience I've only used continuous-time control system analysis/standard frequency domain ...
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MATLAB allmargin() function return multiple GainMargin, but how to identify them on the Bode plot?
I have a high order discrete transfer function model which has the following form. When I use the allmargin function to get the gain margin, I get the following result:
...
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why Type III systems has at least two gain margins?
I heard the following statement https://engineering.stackexchange.com/a/54322/40848
if we have a type III system, or one that has three or more low-frequency poles that we're closing around, then we ...
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Why are the phase indicators different between the open loop bode plot and the closed loop bode plot?
I have an open-loop transfer function G
num=105*conv([1 1],[1 2 43.25]);
den=conv([2 0 0],conv([1 2 82],[1 2 101]));
G=tf(num,den);
and a closed-loop function of G/(1+G). Here are the open-loop bode ...
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What is the effect of the resonant frequency of the system function Porter diagram on the stability of the system and how to analyze it?
I am a novice in automatic control, the theoretical basis is not very good. We have a large electric clamping jaw, single degree of freedom, the motor is controlled by the torque output, the motor has ...
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How to convert PI controller in to differential equation?
I want to convert PI controller into Differential Equation form. How should I do this? Please help me.
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Internal Stability and Small Gain Theorem
I am currently working on a MIMO feedback system and trying to determine its internal stability. The open loop gain of the system is stable and has no internal right half-plane pole-zero cancellations....
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$\mathcal H_2$ norm for LTV system
Preliminary: Consider a stable, strictly causal discrete-time LTI system with state-space model $\left[\begin{array}{c|c}
A & B\\
\hline
C & \pmb{0}
\end{array}\right]$. ...
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Controlling a system in a particular direction
In Discrete-time Control Engineering by Katsuhiko Ogata, it is stated that "A necessary and sufficient condition for complete state controllability is that no cancellation occurs in the pulse ...
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What is the original source of the common Ziegler-Nichols PID tuning coefficients?
In many places, including but not limited to the Wikipedia page about PID controllers, I see the following PID coefficients: $K_P = 0.6K_U$, $K_I = 1.2 K_U / T_U$, and $K_D = 0.075 K_UT_U$. When were ...
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What causes an EUC to propel forwards when leaned forwards?
I have heavily edited the question, as its previous standing was quite hopeless
Thinking about a simple model of a unicycle, where the rider is a uniformly distributed rod and the unicycle just ...
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2
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271
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How to develop the the Backward Euler method for a State Space
I have been trying to develop to solve a state space model in discrete time.
I have the following equation for my state space:
$$\dot{x} = Ax + Bu, $$
I am developping the equation, but I do not ...
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Real-life examples of linear dynamical systems with nonzero D matrix
Which systems that are controlled in real applications are modeled as linear systems
$$
\dot x = Ax + Cu\\
y = Cx + Du
$$
with a nonzero $D$ matrix?
I myself have only been stumbling over systems that ...
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State Space Modeling nonlinear terms of vehicle’s longitudinal motion
My project is to build a software to help drivers achieve ecodriving thanks to optimal control based advices. Consequently, to feed a linear quadratic regulator, vehicle longitudinal equation of ...
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What would the dynamics and measurement operators be in this control theory problem/code, and where can I generate them from?
I'm working on something slightly outside of my scope of work, and I can't figure out if I fully understand what these things mean. Could someone help explain what the dynamics operator and ...
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What is the difference between mathematical and process/control degrees of freedom?
Taking mathematical DOF as:
$$ DOF= N_{vars}-N_{eqs} $$
How would process, or control degrees of freedom be defined as?
Thanks!
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Sensor fusion for IMU
I'm working with MPU-6050 sensor with Raspberry Pi 4. I can read acceleration and gyroscope raw data from the sensor. However I want to get yaw, pitch and roll angles from these data. I tried to ...
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How do you find the gains for a PI controller with a first order plant and 2nd order low pass filter?
How can analytically work out the gains knowing the required bandwidth and damping? The plant to be controlled is first order. The low pass filter is 2nd order in the feedback path.
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Can there be more than one gain margin?
Why would that be the case? How does one determine stability in this case?
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Real examples of complex PID regulators
I am currently developing the C library for easy implementation of PID controllers. Can you give some examples of complex PID controllers from real life? I don't mean a simple DC motor with a speed ...
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Lag compensation with the forth order system
The control system below is with lag compensation. The question asks to find a and T so that the characteristic equation of the ...
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Boeing 747 Autopilot Vertical Speed Function (PID Controller)
I originally asked this over at the math stack-exchange but was told I might have better luck here. I have simply copy-pasted the question.
I am working on a Boeing 747 autopilot control system for an ...
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Linearization about equilibrium point 0 in the presence of unknown input
Consider a SISO non-linear system $$\dot{x} = F(x,u)$$ in which $\vec{0}$ is an equilibrium point. In the process of determining that it is indeed an equilibrium point, the input did not matter at all....
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