MATLAB Examples

Adaptive Cruise Control System Using Model Predictive Control

This example shows how to use a model predictive controller (MPC) to implement an adaptive cruise control (ACC) system.


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Adaptive Cruise Control System

An ACC equipped vehicle (host car) has a sensor, such as radar, that measures the distance to the preceding vehicle in the same lane (lead car), as well as the relative velocity of the lead car. The ACC system operates in two modes: speed control and spacing control.

  • In speed control, the host car travels at a driver-set speed.
  • In spacing control, the host car maintains a safe distance from the lead car.

The ACC system decides which mode to use based on real-time radar measurements. For example, if the lead car is too close, the ACC system switches from speed control to spacing control. Similarly, if the lead car is further away, the ACC system switches from spacing control to speed control. In other words, the ACC system makes the host car travel at a driver-set speed as long as a safe distance is maintained.

In this example, to achieve speed control or spacing control, the ACC system manipulates acceleration.

ACC System Design

Open the Simulink model. The ACC system is modeled using the Adaptive Cruise Control System subsystem block in Simulink.

mdl = 'mpcACCsystem';

The inputs to the ACC system are:

  • Driver-set velocity $V_{set}$
  • Velocity of the host car $V_{host}$
  • Actual distance to the lead car $D_{act}$ (from radar)
  • Velocity of the lead car $V_{lead}$ (from radar)

The output for the ACC system is the acceleration of the host car.

The dynamics between acceleration and velocity are modeled as:

$$ \frac{1}{s(0.5s+1)} $$

which approximates the dynamics of the throttle body and vehicle inertia. The same transfer function applies to both the host car and lead car.

The safe distance between the lead car and the host car is a function of the velocity of the host car, $V_{host}$:

$$ D_{safe} = 10 + 1.4\times V_{host} $$

where 10 (m) is the standstill distance and 1.4 (sec) is the time gap.

The following rules are used to determine the ACC system operating mode:

  • If $D_{act} \geq D_{safe}$, then speed control mode is active. The control goal is to track the driver-set velocity, $V_{set}$.
  • If $D_{act} < D_{safe}$, then spacing control mode is active. The control goal is to maintain the safe distance, $D_{safe}$.

Specify the initial conditions for the two vehicles.

x0_lead = 50;   % initial position for lead car (m)
v0_lead = 25;   % initial velocity for lead car (m/s)

x0_host = 10;   % initial position for host car (m)
v0_host = 20;   % initial velocity for host car (m/s)
a0_host = 0;    % initial acceleration for host car (m/s^2)

Specify the target driver-set velocity in m/s.

v_set = 30;

Define the sample time, Ts, and simulation duration, T, in seconds.

Ts = 0.1;
T = 80;

To approximate a realistic driving environment, vary the acceleration of the lead car during the simulation.

a0_lead.time = (0:0.1:T)';
a0_lead.signals.values = 0.6*sin(a0_lead.time/5);
a0_lead.signals.dimensions = 1;

MPC Structure

In this example, the ACC is implemented using a linear MPC.

ACC = [mdl '/Adaptive Cruise Control System'];

The MPC controller has:

  • Two measured outputs (MO): Spacing error, $e = D_{act}-D_{safe}$, and host car velocity, $V_{host}$. The spacing error should have a lower bound of 0 to maintain the safe distance. The desired host car velocity is the driver-set velocity, $V_{set}$.
  • One manipulated variable (MV): Host car acceleration, $a$. Considering the physical limitations of the vehicle dynamics, the acceleration is constrained to be within $[-3,2]$ ($m/s^2$).
  • One measured disturbance (MD): Lead car velocity, $V_{lead}$, which allows MPC to predict its impact on the spacing error.

Given this MPC structure, define the linear prediction model by linearizing the Simulink model at the initial operating point. This step requires Simulink® Control Design™ software.

Specify analysis points for linearization.

io(1) = linio([ACC '/MPC'],1,'openinput');           % MV: acceleration
io(2) = linio([mdl '/Lead Car/Sum1'],1,'openinput'); % MD: lead velocity
io(3) = linio([ACC '/Sum1'],1,'output');             % OV(1): spacing error
io(4) = linio([mdl '/Host Car'],2,'output');         % OV(2): host velocity

Linearize the plant and obtain a minimum realization of the resulting linear model.

sys = linearize(mdl,io);
sys = minreal(sys);
1 state removed.

Specify the MPC signal types in the plant.

sys = setmpcsignals(sys,'MV',1,'MD',2);

MPC Design

To design a model predictive controller for the plant model, first create an MPC controller using a default prediction horizon (10 steps) and control horizon (2 moves).

mpc1 = mpc(sys,Ts);
-->The "PredictionHorizon" property of "mpc" object is empty. Trying PredictionHorizon = 10.
-->The "ControlHorizon" property of the "mpc" object is empty. Assuming 2.
-->The "Weights.ManipulatedVariables" property of "mpc" object is empty. Assuming default 0.00000.
-->The "Weights.ManipulatedVariablesRate" property of "mpc" object is empty. Assuming default 0.10000.
-->The "Weights.OutputVariables" property of "mpc" object is empty. Assuming default 1.00000.
   for output(s) y1 and zero weight for output(s) y2 

Specify the controller nominal values based on the simulation initial conditions.

mpc1.Model.Nominal.Y(1) = (x0_lead-x0_host) - (10+1.4*v0_host);
mpc1.Model.Nominal.Y(2) = v0_host;
mpc1.Model.Nominal.U(1) = a0_host;
mpc1.Model.Nominal.U(2) = v0_lead;

Specify scale factors based on the operating ranges of the variables.

mpc1.MV.ScaleFactor = 5;      % range of acceleration is 2 - (-3)
mpc1.DV.ScaleFactor = 30;     % assume same as host car speed limit
mpc1.OV(1).ScaleFactor = 10;  % typical spacing error
mpc1.OV(2).ScaleFactor = 30;  % host car ACC speed limit

Specify MV constraints.

mpc1.MV.Min = -3;             % maximum deceleration
mpc1.MV.Max = 2;              % maximum acceleration

Specify OV constraints. To achieve spacing control, set the minimum spacing error constraint to 0.

mpc1.OV(1).Min = 0;

Specify weights. To achieve speed control, use a nonzero weight on the host car velocity.

mpc1.Weights.OV = [0 1];

If the spacing error constraint is active, the controller treats the constraint violation as a higher priority over reference tracking. In this case, the ACC system is in spacing control mode and maintains a safe distance.

If the spacing error constraint is inactive, the controller performs reference tracking. In this case, the ACC system is in speed control mode and achieves the driver-set cruising velocity.

Write the MPC controller to the Simulink block.

set_param([ACC '/MPC'],'mpcobj','mpc1')

Simulation Analysis

Run the simulation with the designed model predictive controller.

-->Converting model to discrete time.
-->Assuming output disturbance added to measured output channel #2 is integrated white noise.
   Assuming no disturbance added to measured output channel #1.
-->The "Model.Noise" property of the "mpc" object is empty. Assuming white noise on each measured output channel.

Plot the simulation result.


In the first 3 seconds, to reach the driver-set velocity, the host car accelerates at full throttle.

From 3 to 13 seconds, the lead car accelerates slowly. As a result, to maintain a safe distance to the lead car, the host car accelerates with a much slower rate.

From 13 to 25 seconds, the host car maintains the driver-set velocity, as shown in the Velocity plot. However, as the lead car reduces speed, the spacing error starts approaching 0 after 20 seconds.

From 25 to 45 seconds, the lead car slows down and then accelerates again. The host car maintains a safe distance from the lead car, as shown in the Distance and Spacing error plots, by adjusting its speed.

From 45 to 56 seconds, the spacing error is above 0. Therefore, the host car achieves the driver-set velocity again.

From 56 to 76 seconds, the deceleration/acceleration sequence from the 25 to 25 second interval is repeated.

In this example, an adaptive cruise control system is designed using model predictive control. The design guarantees that the actual distance between the two vehicles is greater than a safe distance. If the actual distance is sufficiently large, then the design guarantees that the vehicle follows the driver-set velocity. This example demonstrates that the control objectives and constraints required by the ACC system can be achieved using MPC.

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