# Questions tagged [nonlinear-control]

For questions regarding the control of nonlinear dynamical systems with known or unknown nonlinearities.

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### Why the control input for in the operating point is not considered in the control?

One method of controlling a nonlinear system is linearizing the model in an operating point and gain scheduling the controller. The operating point includes a state and an input (the trim input) so ...
32 views

### Control with variable delay plus inverse relationship

As we all (should) know, PID controllers are pretty bad when the system they control isn't linear. In my case, I have a water heater and a pump. I want to control the pump so that the output is at a ...
69 views

### Is it theoretically possible to control an continuously flexible inverted pendulum?

We can control an inverted pendulum relatively easily with PID. We can control a double-inverted pendulum with more sophisticated methods. Lately, a triple inverted pendulum was controlled, with 56 ...
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### Control a plant with a general logistic function like characteristic

I have a "real" plant, which is basically a light bulb, with a characteristic curve which matches the shape of a generalised logistic function I need to control that plant dynamically over ...
96 views

### Use feedforward to control a simple pendulum open loop system

I am currently simulating a simple torque controlled pendulum in simulink (friction accounted for). This and all works like a charm. Now for the control of the system am using the system's ...
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### How could Adrian Bejan's 'Constructal Law' be formulated mathematically?

Adrian Bejan is known for having devised a very interesting theory for the hierarchical and aesthetic structure found in nature, from the branching tree shape of river deltas to the tree shape of ...
117 views

### 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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1 vote
119 views

### 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....
4k views

### Non-Linear Analysis Convergence Problem in Ansys

I am currently conducting a static structural analysis study in Ansys and encountered convergence prolems. I have a very large thermal gradient (almost 600°C) as input from a precedent transient ...
1 vote
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### What's a real life example of linearization of a system around a fixed point

I'm tasked on finding a example of a real non-linear control system. a real paper or publication on a website like the IEEE thats describes the model of the system so I can then linearizy it around a ...
44 views

### Stability properties of controllers with independent control laws applied in underactuated systems

I am interested in designing a GNC controller for a 3DOF underactuated vehicle that follows a path in 2D space. The two available control inputs are the thrust force in the surge direction and a ...
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### Best Techniques to design a cascaded precision position controller

I'm looking to design a cascaded controller to transform a BLDC into a servomotor. The system has a motor current controller in the inner loop, which is controlled by a torque controller, which is ...
47 views

### Block-diagram combining two controlled subsystems

I have two subsystems which are shown in the picture below. One of them is a system of stable and controlled differential equations of a mechanical system. Second is a block that implements a function ...
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### Linearizing nonlinear system for PID control

I have a system where y = 1/x. (y=output, x=input) If I calculate the PID error not by reading y, but by reading 1/y (so linearizing the system), will my system be nicely linearized, and the PID ...
1 vote
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### How could I verify the stability of a real system with non-linearities?

For a closed loop system, I could do the stability margin analysis using linear method like bode diagram, but in reality there are non-linear elements in the system like saturation/rate limits inside ...
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### Definition of BIBO stability of a nonlinear system

I am studying an electric motor whose state-space equations are nonlinear. I am trying to control the system through a closed loop and I would like to verify the BIBO stability. For linear systems, ...
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### PI or PID-regulator for control system with hysteresis relay in inner loop

I have such control system (sorry for rough drawing :) ) $G(s)$ - stable object with proper transfer function. $1/s$ - integrator. I need to clarify, how synthesized PI or PID controller for such ...
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143 views

### How do I study the frequency response of a physical system with Arduino?

I am a control engineering student and I am studying the frequency response of a system, so the Laplace domain, the Bode plot, poles, zeros,etc. ... I have clear grasp of their meaning, but if I think ...
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### Increasing convergence rate using Optimal Control and Pontryagin Maximum Principle

My question is in addition to Tuning the optimal control synthesized according to the Pontryagin maximum/minimum principle and choosing the cost function, but requires help from the mathematical side ...
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### Input signal rescaling block [closed]

The input signal is limited and lies in range $[-U;+U]$. $U$ - unknown. The output signal must be rescaled to be in the range $[-1;+1]$, i.e. is $+1$ if the input is at steady-state $+U$, and $-1$ if ...
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### Nonlinear system with time-optimal control

Given nonlinear system: \begin{cases} \dot{x_1}=x_3+u \\ \dot{x_2}=-x_2+\dot{f} \\ \dot{x_3}=-x_3+x_2 \cdot \alpha \sin(\omega t) \\ \dot{x_4}=-x_4+x_2 \cdot (\frac{16}{\alpha^2}(\sin(\omega t)-\frac{...
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### Fixed end points optimal control problem

Given two points $(t_0,x(t_0)=x^{0})$ and $(t_1,x(t_1)=x^{1})$ in the $(t,x)$ plane, the objective is to find an optimal trajectory $x^{*}(t)$ such that the cost function \label{eq:1} ...
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### Research of transients in nonlinear systems with linear dynamic links

I am having difficulties of this nature. There is a nonlinear system of the following type: I need to analyze analytically the transient process in such a system. The analytical study of the ...
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### Adding phase error to a system based on phase margin

I have a MIMO transfer function and referring to a research work, I have found a phase margin for this MIMO system. I want to check and see the system blow when a phase error greater than the phase ...
304 views

### A clarifying question on Lasalle invariance principle

Given a nonlinear system $$\dot{x}=f(x),~x(0)=x_0 \tag{1}$$ where $f\in{\mathcal{C}^{1}}:D\to\mathbb{R}^{n}$. The Lasalle invariance theorem statement goes as follows: Let \$...
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### Control of a nonlinear static MIMO System

I am currently writing my master thesis and trying to design a controller for my system. However, the system is somewhat unconventional. It has a large number of inputs and outputs, is static, non-...
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### Which course to take? Optimal control? Nonlinear control? [closed]

I have tried to compare two courses, and there seems to be some overlap, but not as much. Which method is better when controlling a nonlinear system? Also, what is the main difference between the two?
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