DE102024204803B3 - Device and method for controlling a process with a controller depending on a state variable of the process - Google Patents

Abstract

Apparatus and method for controlling a process (110) with a controller (112) depending on a state variable of the process (110), wherein the process (110) is executed on a first device, wherein the controller (112) is executed on a second device, wherein a communication network (100) connects the first device and the second device, the method comprising determining (212) the value of the quadratic Lyapunov function for a value of the state variable, and taking an action (214) if it is determined that the value of the quadratic Lyapunov function exceeds a threshold value, and otherwise not taking the action, the action comprising reducing the data traffic on the communication network (100) and/or stopping the process (110) and/or switching on a controller for the process (110) on the first device and/or shifting the controller (112) from the second device to a third device, wherein the communication network (100) connects the first device and the third Device, wherein a latency of the communication network (100) between the first device and the third device is lower than the latency between the first device and the second device (104).

Description

background

The invention relates to a device and a method for controlling a process with a controller depending on a state variable of the process.

In a networked control system, a process involving a controlled system is controlled in a control loop by a controller over a communications network from a remote location. A major challenge for this type of control system is latency, the delay between the controller and the controlled system. Latency can vary over time. This delay can actually destabilize and degrade the performance of the control loop.

Disclosure of the invention

A method for controlling a process with control depending on a state variable of the process, wherein the process is executed on a first device, wherein the control is executed on a second device, wherein a communication network connects the first device and the second device, the method comprising determining the value of the quadratic Lyapunov function of a value of the state variable, and taking an action if it is determined that the value of the quadratic Lyapunov function exceeds a threshold, and otherwise not taking the action, wherein the action comprises reducing data traffic on the communication network and/or stopping the process and/or switching on control for the process on the first device and/or shifting control from the second device to a third device, wherein the communication network connects the first device and the third device, wherein a latency of the communication network between the first device and the third device is lower than the latency between the first device and the second device. The method monitors the robustness of the process based on the value of the quadratic Lyapunov function. The method detects whether the process is losing stability based on the value of the quadratic Lyapunov function of the state variable's value. The controller and the process are running on different devices in the communication network. Due to communication network problems, missing control inputs from the controller to the process can occur. Missing control inputs from the controller to the process can lead to process instability. The quadratic Lyapunov function of the state variable's value considers missing control inputs from the controller to the process as a disturbance. If it is determined that the process is losing stability, the method takes action.

The method can be carried out on the first device, i.e. on the same device as the process.

The method can be carried out on the second device, i.e. on the same device as the controller.

The method may be executed on the third device, i.e., on the device that can control the process with lower latency than the current controller can provide.

The method can be executed on a fourth device, wherein the communication network connects the first device and the fourth device. This means that the method can be executed on a separate monitoring device in the communication network.

A device for controlling a process with a control depending on a state variable of the process is designed to carry out the method.

According to one example, the apparatus comprises the first apparatus, the first apparatus being configured to determine the value of the quadratic Lyapunov function of the value of the state variable, and to take an action if it is determined that the value of the quadratic Lyapunov function exceeds a threshold, and otherwise not to take the action.

According to one example, the device comprises the second device, wherein the second device is configured to determine the value of the quadratic Lyapunov function of the value of the state variable. and to take an action if it is determined that the value of the quadratic Lyapunov function exceeds a threshold, and otherwise not to take the action.

According to one example, the apparatus comprises the third apparatus, wherein the third apparatus is configured to determine the value of the quadratic Lyapunov function of the value of the state variable, and to take an action if it is determined that the value of the quadratic Lyapunov function exceeds a threshold, and otherwise not to take the action.

According to one example, the apparatus comprises the fourth apparatus, wherein the fourth apparatus is configured to determine the value of the quadratic Lyapunov function of the value of the state variable, and to take an action if it is determined that the value of the quadratic Lyapunov function exceeds a threshold, and otherwise not to take the action.

A computer program may be provided, the computer program comprising computer-readable instructions which, when executed by a computer, cause the computer to carry out the method.

• 1 zeigt schematisch ein Kommunikationsnetzwerk,
• 2 zeigt ein Ablaufdiagramm, das Schritte eines Verfahrens zur Steuerung eines Prozesses mit einer Steuerung in Abhängigkeit von einer Zustandsvariablen des Prozesses umfasst,
• 3 zeigt ein beispielhaftes System, das den Prozess ausführt,
• 4 zeigt ein erstes beispielhaftes Verhalten einer quadratischen Ljapunow-Funktion,
• 5 zeigt ein zweites beispielhaftes Verhalten der quadratischen Ljapunow-Funktion.

Further examples can be found in the following description and drawing. In the drawing:

• 1 shows a schematic of a communication network,
• 2 shows a flowchart comprising steps of a method for controlling a process with a controller depending on a state variable of the process,
• 3 shows an example system that executes the process,
• 4 shows a first exemplary behavior of a quadratic Lyapunov function,
• 5 shows a second exemplary behavior of the quadratic Lyapunov function.

1 shows a schematic diagram of a communication network 100.

The communication network 100 includes a first device 102 and a second device 104.

The communication network 100 connects the first device 102 and the second device 104.

The communication network 100 may include multiple devices. 1 shows, by way of example, a third device 106 and a fourth device 108.

The communication network 100 connects the first device 102 and the third device 106. The communication network 100 connects the first device 102 and the fourth device 104.

According to one example, a process 110 is controlled by a controller 112 for controlling the process 110. At least one sensor 114 is configured to monitor the process 110. At least one actuator 116 is configured to control the process 110. The first device 102 is connected to the sensor 114 and the actuator 116. The controller 112 is executed on the second device 104.

With respect to the process 110, the first device 102 is a local device. The local device performs input operations with the at least one sensor 114 and/or output operations with the at least one actuator 116. For example, the local device reads inputs from the at least one sensor 114 to monitor the process 110 or an environment of the process 110. The inputs are provided to the controller. The controller 112 controls the process depending on the inputs. For example, the local device actuates the at least one actuator 116 to control the process 110 according to an output of the controller 112.

The communication network 100 includes, for example, a CAN (Controller Area Network) bus. The communication network 100 includes, for example, a local area network (LAN). The communication network 100 includes, for example, a wireless local area network (WLAN). The communication network 100 includes, for example, a wide area network (WAN).

The communication network 100 may include a combination of CAN, LAN, WLAN, WAN.

The first device 102, the second device 104, the third device 106, and the fourth device 108 may comprise a microcontroller and a memory, in particular a transient and a non-volatile memory. For example, a computer program may be provided on the transient and non-volatile memory, wherein the computer program comprises computer-readable instructions that, when executed by a computer, e.g., the microcontroller, cause the computer to perform a method for controlling the process 110 with the controller 112.

According to the example, the process 110 is represented and linearized by a system in the form of a discrete state space: $$x_{k+1}=A{x}_k+B{u}_k$$ where x _k represents a value of the state variable of the process 110, u _k represents a value of the control input of the process 110, A represents the system matrix of the process 110, and B represents the input matrix of the process 110.

Assuming that A is asymptotically stable, there exists a positive semidefinite matrix P such that $$A^{T}PA-P=-Q$$ where Q is a symmetric positive definite matrix. The Lyapunov function for this system is $$V\left(x\right)=x^{T}Px$$

The controller 112 according to the example is a state feedback controller $$u_k=-K{x}_k$$ where K is the control gain matrix.

For example, the states of process 110 are measurable, observable or estimable.

2 shows a flowchart comprising steps of the method for controlling the process 110, wherein the controller 112 is dependent on a state variable 202 of the process 110.

In the example, the at least one sensor 114 sends a value x of the state variable 202 to the controller 112 via the communication network 100. The at least one sensor 114 monitors the process 110 to determine the value x of the state variable 202.

In a step 204, the controller 112 determines a value u of a control input 206 for the process 110 depending on the value x of the state variable 202.

In the example, the controller 112 sends the value u of the control input 206 to the at least one actuator 116 via the communication network 100.

In a step 208, the process 110 is executed depending on the received value u of a control input 206. The at least one actuator is actuated according to the value u of the control input 206 in order to execute the process 110 according to the received value u of the control input 206.

Steps 202, 204, 206, 208 are repeatedly executed with controller 112 to control process 110.

The method for controlling process 110 with controller 112 is described using the example of a monitoring application 209. The monitoring application 209 is designed to monitor the state variable 202 of process 110.

The monitoring application 209 is designed to determine whether or not an action should be taken depending on the state variable 202 of the process 110.

The measure may consist of reducing the data traffic in the communication network 100.

The action may include stopping the process 110.

The measure may include switching on a controller for the process 110 on the first device 102.

The action may include moving the controller 104 from the second device 104 to the third device 106.

The monitoring application 209 may be executed on the first device 102, the second device 104, the third device 106, or the fourth device 108.

The method for controlling the process 110 with the controller 112 includes a step 210.

Step 210 includes receiving the value x of the state variable 202 at the monitoring application 209.

The method for controlling the process 110 with the controller 112 includes a step 212.

Step 212 includes determining the value V(x) of the quadratic Lyapunov function $$V\left(x\right)=x^{T}Px$$ for the value x of the state variable 202, where the system is quadratically bounded, ie: $$x^{T}Px>\eta \to {\left(A{x}_k+BK{d}_k\right)}^{T}P\left(A{x}_k+BK{d}_k\right)-x_k^{T}P{x}_k<\mathrm{0,}\forall \Vert d\Vert \le \delta and\forall k\ge 0$$ where η is a threshold and d _k is a disturbance.

The quadratic boundedness property guarantees robustness against bounded perturbations, since for any value outside the ellipsoid $${\epsilon }_{\eta }=\left\{x\in {ℝ}^n|x^{T}Px\le \eta \right\}$$ the controller 112 is able to counteract the effects of the disturbance d _k .

According to the example, the disturbance d _k may be a missing value u of the control input 206. The value u of the control input 206 may be missing due to problems in the communication network 100.

According to the example, the disturbance d _k is acceptable until the value V(x) of the quadratic Lyapunov function exceeds the threshold η, i.e. V(x) > η.

According to the example, the threshold value η is given for the method.

For example, a latency of the communication network 100 is modeled as disturbances d _k , and as long as the disturbances d _k are limited, the controller 112 brings the process 110, ie the system, back to stability.

Instead of the latency, or in addition to the latency, the disturbances d _k can be used to model and monitor the network delay of the communication network 100, or to model uncertainties or other disturbances.

The method for controlling the process 110 with the controller 112 includes a step 214.

Step 214 includes taking the action if it is determined that the value V(x) of the quadratic Lyapunov function exceeds the threshold η, ie, V(x) > η, and otherwise not taking the action.

For example, the monitoring application 209 reduces the data traffic in the communication network 100, or requests a reduction.

For example, the monitoring application 209 stops the process or requests that the process 110 be stopped.

For example, the monitoring application 209 turns on or requests control for the process 110 on the first device 102.

For example, the monitoring application 209 moves the control 104 from the second device 104 to the third device 106, or requests this.

3 shows an exemplary system 300 that performs the process, an inverted pendulum 300.

The physical model of the inverted pendulum is given by the following system of second-order ordinary differential equations: $$L\ddot{\Theta }=g\text{ sin }\mathrm{\Theta }-\ddot{\text{y}}\text{ cos }\mathrm{\Theta }-\frac{k}{m}L\dot{\Theta }$$ $$\left(M+m\right)\ddot{\text{y}}=mL{\dot{\Theta }}^2\text{ sin }\mathrm{\Theta }-mL\ddot{\Theta }\text{ cos }\mathrm{\Theta }-b\dot{\text{y}}+F$$ where the mass of the rope is negligible, and
m [Kg]: mass of the pendulum 302,
M [Kg]: Mass of the car 304,
L [m]: length of the pendulum from the pin to the pendulum body,
b [Ns/m]: friction coefficient of the carriage 304,
k [Nsm/Rad]: friction coefficient of the pendulum 302,
Θ [wheel]: angle formed by the pendulum with the vertical axes passing through the pin, Θ = 0 represents the upright position,
y [m]: position of the carriage 304,
F [N]: force exerted on the car 304,
g=9.81 [m/s ² ]: acceleration due to gravity.

The inverted pendulum 300 is modeled for the state space variables x ¹ = θ,x ² = Θ̇, x ³ = y, x ⁴ = ẏ and approximations such as Θ ≈ 0 by $$\dot{\text{x}}=Ax+BF$$ where $$A=\left[\begin{array}{cccc}0& 1& 0& 0\\ \frac{\overline{M}g}{LM}& \frac{\overline{M}\stackrel{}{\left(\frac{kL}{m}\right)}}{LM}& 0& \frac{b}{LM}\\ 0& 0& 0& 1\\ -\frac{gm}{M}& \frac{\left(\frac{k}{m}\right)}{M}& 0& -\frac{b}{M}\end{array}\right]$$ where M = M + m and the control input u is the force F exerted on the carriage 304. $$B={\left[0-\frac{1}{ML}0\frac{1}{M}\right]}^T$$

4 shows an example behavior of the quadratic Lyapunov function V(x _k ) for the inverted pendulum and the threshold value η. According to one example, the threshold value η = 10 is used. Successive perturbations d _k are caused by a missing value u of the control input. The control input in the example is the force F applied to the carriage 304. The missing force F applied to the carriage 304 causes the perturbations.

According to the example, a received control input 402 is followed by 22 consecutive missing control inputs 404. 4 shows time steps k=0, ..., 45. 4 shows a first sequence of 22 consecutive missing control inputs 404 between a first received control input 402 and a second received control input 402. 4 shows a second sequence of 22 consecutive missing control inputs 404 between the second received control input 402 and a third received control input 402. None of the illustrated missing control inputs 404 exceeds the threshold η. Thus, no action is taken according to the methods described above.

5 shows the exemplary behavior of the quadratic Lyapunov function V(x _k ), where a value 502 of a consecutively missing control input 404 exceeds the threshold η. In the example, the 25th consecutive missing control input 404 exceeds the threshold: v(x ₂₅ ) > η. In this case, according to the method described above, at least one of the measures described above is taken to avoid a loss of stability.

The method is applicable to various application areas ranging from software-defined vehicles, the Internet of Things (IoT), intelligent IoT, IIoT, to edge cloud-based control and cloud-based control.

For example, process 110 includes controlling a computer-controlled machine, such as a software-defined vehicle.

The action taken may be selected depending on the requirements of the process 110 and the capabilities of the communication network 100 and/or the third device 106 with respect to the latency in the communication between the controller 112 and the process 110.

Regardless of the area of application, the procedure provides a framework for implementing measures that lead to robust control.

Claims (11)

Method for controlling a process (110) with a controller (112) depending on a state variable of the process (110), characterized in that the process (110) is executed on a first device (102), wherein the controller (112) is executed on a second device (104), wherein a communication network (100) connects the first device (102) and the second device (104), the method comprising determining (212) the value of the quadratic Lyapunov function for a value of the state variable, and taking an action (214) if it is determined that the value of the quadratic Lyapunov function exceeds a threshold value, and otherwise not taking the action, the action comprising reducing the data traffic on the communication network (100) and/or stopping the process (110), and/or switching on a controller for the process (110) on the first device (102), and/or shifting the controller (112) from the second device (104) to a third device (106), wherein the communication network (100) connects the first device (102) and the third device (106), wherein a latency of the communication network (100) between the first device (102) and the third device (106) is lower than the latency between the first device (102) and the second device (104). Procedure according to Claim 1 , characterized by carrying out the method on the first device (102). Procedure according to Claim 1 , characterized by carrying out the method on the second device (104). Procedure according to Claim 1 , characterized by carrying out the method on the third device (106). Procedure according to Claim 1 characterized by executing the method on a fourth device (108), wherein the communication network (100) connects the first device (102) and the fourth device (108). Device for controlling a process (110) with a controller (112) as a function of a state variable of the process (110), characterized in that the device is designed to carry out the method according to one of the preceding claims. Device according to Claim 6 , characterized in that the device comprises the first device (102), the first device (102) being adapted to determine the value of the quadratic Lyapunov function of the value of the state variable, and to take an action if it is determined that the value of the quadratic Lyapunov function exceeds a threshold value, and otherwise to take no action. Device according to Claim 6 , characterized in that the device comprises the second device (104), wherein the second device (104) is adapted to determine the value of the quadratic Lyapunov function of the value of the state variable, and to take an action if it is determined that the value of the quadratic Lyapunov function exceeds a threshold value, and otherwise to take no action. Device according to Claim 6 , characterized in that the device comprises the third device (106), wherein the third device (106) is adapted to determine the value of the quadratic Lyapunov function of the value of the state variable, and to take an action if it is determined that the value of the quadratic Lyapunov function exceeds a threshold value, and to take no action otherwise. Device according to Claim 6 , characterized in that the device comprises a fourth device (108), wherein the fourth device (108) is adapted to determine the value of the quadratic Lyapunov function of the value of the state variable, and taking an action if it is determined that the value of the quadratic Lyapunov function exceeds a threshold value, and otherwise taking no action, wherein the communication network (100) is adapted to connect the first device (102) and the fourth device (108). Computer program, characterized in that the computer program comprises computer-readable instructions which, when executed by a computer, cause the computer to carry out the method according to one of the Claims 1 until 5 to execute.