【Practical Exercise】Simulink-Based Modeling of a PID Double-Arm Robotic Hand
发布时间: 2024-09-14 04:50:37 阅读量: 35 订阅数: 22
# 2.1 The Principle and Design of PID Controllers
### 2.1.1 Structure and Principle of PID Controllers
A PID controller is a type of feedback control system that measures the output of the controlled object, compares it with the desired output, calculates the error, and adjusts the control output based on the proportional, integral, and derivative values of the error. The structure of a PID controller is as follows:
```mermaid
graph LR
subgraph PID Controller
e[Error] --> p[Proportional] --> u[Control Output]
e --> i[Integral] --> u
e --> d[Differential] --> u
end
```
Where:
* e: Error, the difference between the desired and actual output
* p: Proportional coefficient, used to adjust the proportional relationship between the control output and the error
* i: Integral coefficient, used to eliminate steady-state errors
* d: Differential coefficient, used to predict the trend of error changes
The output calculation formula for a PID controller is:
```
u(t) = Kp * e(t) + Ki * ∫e(t)dt + Kd * de(t)/dt
```
Where:
* Kp, Ki, Kd are the proportional, integral, and differential coefficients respectively
* t is the time
# 2. Simulink Modeling of PID Control
### 2.1 PID Controller Principle and Design
#### 2.1.1 Structure and Principle of PID Controllers
A PID controller is a feedback control algorithm used to minimize the error between the system output and the desired output. Its structure is shown in the following diagram:
```mermaid
graph LR
subgraph PID Controller
A[Setpoint] --> B[Error Calculation]
B --> C[Proportional Gain]
B --> D[Integral Gain]
B --> E[Differential Gain]
C --> F[Proportional Term]
D --> G[Integral Term]
E --> H[Differential Term]
F --> I[Output]
G --> I
H --> I
end
```
The error calculation module calculates the error between the setpoint and the actual output. The proportional gain, integral gain, and differential gain modules calculate the proportional, integral, and differential terms, respectively. The output module sums these three terms to obtain the controller's output.
#### 2.1.2 PID Parameter Tuning Methods
The parameters of a PID controller (proportional gain, integral gain, differential gain) ***mon tuning methods include:
***Ziegler-Nichols Method:** Estimates PID parameters based on the parameters of the system's step response curve.
***Cohen-Coon Method:** Calculates PID parameters based on the poles and zeros of the system's transfer function.
***Trial and Error Method:** Optimizes control effects by continuously adjusting PID parameters.
### 2.2 Simulink PID Controller Modeling
#### 2.2.1 Using the PID Controller Module
Simulink provides a PID controller module that makes it easy to implement PID control. The module's inputs include the setpoint, actual output, and parameters (proportional gain, integral gain, differential gain). The output is the controller's output.
```
% Setpoint
ref = 1;
% Actual Output
y = 0.5;
% PID Parameters
Kp = 1;
Ki = 0.1;
Kd = 0.01;
% Create PID Controller Module
pid = pid(Kp, Ki, Kd);
% Calculate Controller Output
u = pid(ref, y);
```
#### 2.2.2 Setting PID Parameters and Simulation
Setting PID parameters requires adjustment according to the characteristics of the system. You can use the trial and error method or other tuning methods to determine the optimal parameters.
```
% Set PID Parameters
pid.Kp = 1;
pid.Ki = 0.1;
pid.Kd = 0.01;
% Simulate PID Controller Response
t = 0:0.1:10;
ref = ones(size(t));
y = zeros(size(t));
for i =
```
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